{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 2 qubits which prepares the following quantum state from |00>:\n\n  |00>: -0.679592598898328 + 0i\n  |01>: -0.579526359718494 + 0i\n  |10>: 0.12186683113463 + 0i\n  |11>: -0.432956780040746 + 0i\n\nAs a Python list: [(-0.6795925988983277+0j), (-0.5795263597184941+0j), (0.12186683113462968+0j), (-0.4329567800407461+0j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 2 qubits which prepares the following quantum state from |00>:\n\n  |00>: 0.186920303564353 + 0i\n  |01>: -0.259805218936697 + 0i\n  |10>: -0.469077541147975 + 0i\n  |11>: 0.823121077800365 + 0i\n\nAs a Python list: [(0.18692030356435274+0j), (-0.25980521893669684+0j), (-0.46907754114797484+0j), (0.8231210778003653+0j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 2 qubits which prepares the following quantum state from |00>:\n\n  |00>: 0.639200948222883 + 0i\n  |01>: 0.706432910712519 + 0i\n  |10>: -0.303928322989272 + 0i\n  |11>: 0.00150497114086059 + 0i\n\nAs a Python list: [(0.6392009482228831+0j), (0.7064329107125186+0j), (-0.3039283229892722+0j), (0.0015049711408605866+0j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 2 qubits which prepares the following quantum state from |00>:\n\n  |00>: 0.574227449666636 + 0i\n  |01>: 0.254741853186036 + 0i\n  |10>: -0.663806107729038 + 0i\n  |11>: -0.405870515837649 + 0i\n\nAs a Python list: [(0.5742274496666363+0j), (0.25474185318603626+0j), (-0.6638061077290385+0j), (-0.4058705158376486+0j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 2 qubits which prepares the following quantum state from |00>:\n\n  |00>: -0.809531137010344 + 0i\n  |01>: -0.0871958058075818 + 0i\n  |10>: 0.391728458210054 + 0i\n  |11>: -0.428491592319709 + 0i\n\nAs a Python list: [(-0.8095311370103443+0j), (-0.08719580580758181+0j), (0.3917284582100543+0j), (-0.4284915923197086+0j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 3 qubits which prepares the following quantum state from |000>:\n\n  |000>: -0.293090903992018 + 0.113854542909366i\n  |001>: -0.389870632729889 + 0.0505618808386182i\n  |010>: -0.096451188049864 + -0.347614839272334i\n  |011>: 0.188568414279942 + 0.300183583779644i\n  |100>: 0.143528302940378 + -0.260419701449508i\n  |101>: -0.18999779480164 + 0.433805476427909i\n  |110>: -0.235632342662862 + 0.262041937068119i\n  |111>: 0.149757118346311 + 0.177344838550708i\n\nAs a Python list: [(-0.293090903992018+0.11385454290936582j), (-0.38987063272988914+0.05056188083861817j), (-0.09645118804986401-0.34761483927233394j), (0.188568414279942+0.3001835837796442j), (0.14352830294037786-0.26041970144950766j), (-0.18999779480164006+0.43380547642790945j), (-0.23563234266286223+0.2620419370681189j), (0.14975711834631136+0.17734483855070773j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 3 qubits which prepares the following quantum state from |000>:\n\n  |000>: -0.0223108790295294 + 0.418871600290631i\n  |001>: 0.111837995193444 + 0.41813350561919i\n  |010>: 0.105287856950065 + -0.0401135003229527i\n  |011>: 0.0688561883548244 + 0.218966751731077i\n  |100>: 0.518973107299657 + -0.0851846602869223i\n  |101>: 0.228989737545292 + 0.0878546353210152i\n  |110>: 0.373006844791029 + 0.18706304663995i\n  |111>: -0.123662502756251 + 0.21250846836038i\n\nAs a Python list: [(-0.02231087902952944+0.41887160029063114j), (0.11183799519344445+0.4181335056191901j), (0.10528785695006458-0.040113500322952717j), (0.06885618835482443+0.21896675173107702j), (0.5189731072996567-0.08518466028692227j), (0.2289897375452919+0.08785463532101523j), (0.3730068447910293+0.1870630466399496j), (-0.1236625027562512+0.21250846836037968j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 3 qubits which prepares the following quantum state from |000>:\n\n  |000>: -0.408000230667865 + -0.201128544815899i\n  |001>: -0.0652720772663185 + 0.195159960190748i\n  |010>: 0.198266306193278 + 0.100919334396127i\n  |011>: -0.0667724721289298 + 0.509078581932386i\n  |100>: -0.322657309165835 + 0.125975947223743i\n  |101>: -0.346364819458066 + -0.132527455279334i\n  |110>: 0.173147861375955 + -0.32292615452877i\n  |111>: 0.162642067033587 + -0.139275777201408i\n\nAs a Python list: [(-0.4080002306678651-0.20112854481589865j), (-0.0652720772663185+0.19515996019074758j), (0.19826630619327784+0.10091933439612737j), (-0.0667724721289298+0.5090785819323861j), (-0.3226573091658347+0.12597594722374333j), (-0.3463648194580661-0.1325274552793345j), (0.17314786137595486-0.3229261545287705j), (0.16264206703358686-0.13927577720140788j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 3 qubits which prepares the following quantum state from |000>:\n\n  |000>: -0.143817329197262 + 0.343684577779252i\n  |001>: -0.21443561033101 + -0.133348685501335i\n  |010>: -0.334952591843656 + -0.0973057857396408i\n  |011>: 0.436116264841982 + 0.474026063336211i\n  |100>: 0.104502169391981 + 0.0139796508534925i\n  |101>: -0.293039458911186 + -0.295172226958813i\n  |110>: -0.0434259748783397 + -0.217019580860581i\n  |111>: -0.11119261690854 + 0.124141895003058i\n\nAs a Python list: [(-0.14381732919726198+0.3436845777792518j), (-0.21443561033100997-0.13334868550133466j), (-0.3349525918436561-0.09730578573964081j), (0.4361162648419824+0.47402606333621106j), (0.1045021693919815+0.013979650853492499j), (-0.29303945891118616-0.29517222695881284j), (-0.04342597487833974-0.21701958086058093j), (-0.11119261690853981+0.1241418950030576j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 3 qubits which prepares the following quantum state from |000>:\n\n  |000>: 0.0263830304666013 + 0.0712483819039682i\n  |001>: -0.461960743745515 + -0.0032873920362999i\n  |010>: -0.132470318633408 + 0.124055126720062i\n  |011>: 0.243617850265975 + 0.00176159240610609i\n  |100>: -0.126299428896454 + 0.157973286565687i\n  |101>: 0.127536883879947 + 0.0234428899609667i\n  |110>: -0.440831047854746 + -0.00395460841683894i\n  |111>: -0.59719913612353 + 0.282491517387988i\n\nAs a Python list: [(0.026383030466601287+0.07124838190396823j), (-0.46196074374551505-0.0032873920362999015j), (-0.13247031863340838+0.12405512672006185j), (0.24361785026597513+0.0017615924061060932j), (-0.12629942889645449+0.157973286565687j), (0.127536883879947+0.02344288996096675j), (-0.44083104785474575-0.003954608416838937j), (-0.5971991361235305+0.28249151738798844j)]\n\nRequirements:\n- You may use QuantumCircuit.initialize(statevector, qubits) or any standard gates.\n- Ensure the statevector is normalized (np.linalg.norm == 1) before passing to initialize().\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 4 qubits which prepares the following quantum state from |0000>:\n\n  |0000>: 0.380319162653963 + 0.147081483976425i\n  |0001>: 0.0235049113306221 + 0.36537115002118i\n  |0010>: -0.118453388724446 + -0.0358030091740671i\n  |0011>: -0.155636174947755 + -0.129565999228764i\n  |0100>: 0.0334774058860543 + -0.154937187528018i\n  |0101>: 0.21731595619605 + 0.305001025177836i\n  |0110>: 0.028825248983892 + -0.0658793693596151i\n  |0111>: -0.0727531656405414 + -0.0949261949293224i\n  |1000>: 0.216571204668631 + -0.0711622018621831i\n  |1001>: -0.248451019939225 + 0.155995982801593i\n  |1010>: 0.213041903296148 + 0.0639045383540883i\n  |1011>: -0.174225682774892 + -0.247058930857157i\n  |1100>: 0.117402485774665 + 0.0596873350197036i\n  |1101>: 0.0794265014870999 + 0.0683975521517882i\n  |1110>: -0.0710025277412068 + 0.0587451627545717i\n  |1111>: 0.3756180148078 + -0.0411407904599613i\n\nAs a Python list: [(0.3803191626539635+0.14708148397642468j), (0.023504911330622144+0.3653711500211804j), (-0.1184533887244464-0.03580300917406714j), (-0.15563617494775453-0.12956599922876383j), (0.033477405886054294-0.15493718752801755j), (0.2173159561960499+0.30500102517783556j), (0.028825248983892025-0.06587936935961514j), (-0.07275316564054142-0.0949261949293224j), (0.21657120466863095-0.07116220186218314j), (-0.2484510199392254+0.15599598280159335j), (0.21304190329614778+0.0639045383540883j), (-0.174225682774892-0.24705893085715683j), (0.1174024857746651+0.05968733501970361j), (0.07942650148709994+0.06839755215178815j), (-0.07100252774120679+0.058745162754571714j), (0.3756180148077997-0.041140790459961336j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 4 qubits which prepares the following quantum state from |0000>:\n\n  |0000>: -0.203848151383009 + -0.0927042919495607i\n  |0001>: -0.341038627922005 + -0.107585978539975i\n  |0010>: 0.342024611975759 + 0.07444030057774i\n  |0011>: 0.110782320871863 + -0.164749817657944i\n  |0100>: 0.0910673711806082 + -0.0929441150596542i\n  |0101>: -0.0920940836831661 + 0.0811041603569203i\n  |0110>: 0.139605336700525 + 0.0462282032770101i\n  |0111>: 0.475806765535883 + 0.0635941571198202i\n  |1000>: -0.121610979003811 + 0.0973663990270746i\n  |1001>: -0.257367908930994 + 0.0874187294014403i\n  |1010>: 0.155108038934298 + 0.0683506226720974i\n  |1011>: 0.0406783534411015 + -0.219417451849745i\n  |1100>: -0.00628627547045005 + -0.317123517798357i\n  |1101>: 0.0782777596301891 + -0.115550063116454i\n  |1110>: 0.0744203996228916 + 0.254043952346624i\n  |1111>: -0.0955803530386439 + 0.00104460498121271i\n\nAs a Python list: [(-0.2038481513830095-0.09270429194956072j), (-0.34103862792200534-0.10758597853997542j), (0.3420246119757591+0.07444030057774004j), (0.11078232087186321-0.1647498176579439j), (0.09106737118060818-0.0929441150596542j), (-0.09209408368316609+0.08110416035692032j), (0.1396053367005254+0.04622820327701011j), (0.47580676553588286+0.06359415711982025j), (-0.12161097900381139+0.09736639902707463j), (-0.257367908930994+0.08741872940144034j), (0.15510803893429792+0.06835062267209739j), (0.040678353441101454-0.21941745184974548j), (-0.006286275470450046-0.317123517798357j), (0.07827775963018908-0.1155500631164541j), (0.07442039962289161+0.25404395234662414j), (-0.09558035303864389+0.0010446049812127126j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 4 qubits which prepares the following quantum state from |0000>:\n\n  |0000>: 0.0340111462345571 + 0.201443607741877i\n  |0001>: -0.0879884647077708 + -0.288305748269509i\n  |0010>: -0.154648524370015 + -0.206232872020556i\n  |0011>: -0.032306644146494 + 0.359028350126025i\n  |0100>: 0.0235121883925116 + 0.120985761026209i\n  |0101>: -0.170989191853837 + 0.145451805205799i\n  |0110>: 0.0369588076718125 + -0.00844270969064321i\n  |0111>: -0.0431071635800599 + -0.300867275652751i\n  |1000>: 0.146125862230144 + -0.0252058087108994i\n  |1001>: 0.113680197300941 + 0.202011840633238i\n  |1010>: -0.559973300926891 + 0.0147559844569373i\n  |1011>: 0.00996691852945253 + -0.0569572537734988i\n  |1100>: 0.0325854932980773 + -0.200321452256826i\n  |1101>: -0.159381848798517 + -0.139515110256624i\n  |1110>: 0.0954492232059957 + -0.0442865434058256i\n  |1111>: 0.133307110048415 + -0.0620988099483254i\n\nAs a Python list: [(0.034011146234557144+0.20144360774187653j), (-0.08798846470777083-0.28830574826950867j), (-0.15464852437001497-0.20623287202055576j), (-0.03230664414649398+0.35902835012602513j), (0.023512188392511593+0.12098576102620918j), (-0.17098919185383735+0.14545180520579878j), (0.03695880767181247-0.008442709690643214j), (-0.04310716358005985-0.30086727565275106j), (0.14612586223014398-0.025205808710899388j), (0.11368019730094106+0.20201184063323815j), (-0.5599733009268911+0.01475598445693733j), (0.009966918529452525-0.05695725377349875j), (0.03258549329807733-0.20032145225682632j), (-0.15938184879851724-0.13951511025662364j), (0.09544922320599565-0.0442865434058256j), (0.13330711004841525-0.06209880994832539j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 4 qubits which prepares the following quantum state from |0000>:\n\n  |0000>: 0.24508326102276 + 0.140120017127918i\n  |0001>: 0.17055509352566 + -0.109536396788814i\n  |0010>: -0.0809522962282046 + 0.246722211575361i\n  |0011>: -0.243829486672712 + 0.0928948547377172i\n  |0100>: -0.0559927976391919 + 0.102460938496673i\n  |0101>: -0.198963679319638 + -0.0459028840626909i\n  |0110>: 0.0952649422097255 + 0.155618811738713i\n  |0111>: 0.11084768094051 + -0.108835073729598i\n  |1000>: -0.113317393559721 + 0.173645319443917i\n  |1001>: -0.132009167686583 + -0.162767055069367i\n  |1010>: -0.19707611486958 + -0.007700319143285i\n  |1011>: 0.350915594709976 + -0.130606824072741i\n  |1100>: 0.0533321906031849 + 0.0227108256610709i\n  |1101>: 0.0633246241025911 + 0.233558847864622i\n  |1110>: 0.24231203551491 + 0.404334996014685i\n  |1111>: -0.283629798838512 + 0.0193670299878013i\n\nAs a Python list: [(0.24508326102275957+0.14012001712791777j), (0.17055509352565984-0.10953639678881393j), (-0.08095229622820459+0.24672221157536134j), (-0.24382948667271218+0.09289485473771715j), (-0.055992797639191884+0.1024609384966734j), (-0.19896367931963796-0.04590288406269094j), (0.09526494220972549+0.1556188117387127j), (0.11084768094051049-0.10883507372959762j), (-0.11331739355972077+0.17364531944391692j), (-0.13200916768658322-0.16276705506936726j), (-0.1970761148695805-0.007700319143285003j), (0.35091559470997574-0.13060682407274118j), (0.05333219060318489+0.022710825661070855j), (0.06332462410259108+0.23355884786462205j), (0.24231203551491+0.40433499601468537j), (-0.28362979883851214+0.01936702998780128j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 4 qubits which prepares the following quantum state from |0000>:\n\n  |0000>: 0.083833355012308 + 0.0946798570225192i\n  |0001>: -0.144336036208174 + 0.117305891599423i\n  |0010>: 0.14695618078731 + -0.253893552767962i\n  |0011>: 0.0659457445691654 + 0.0690665640845064i\n  |0100>: 0.0702944956887821 + -0.048162188736309i\n  |0101>: 0.103300391659125 + 0.0653276040903567i\n  |0110>: 0.0878855351312364 + 0.0200052376129196i\n  |0111>: 0.149109300891841 + 0.315424227459824i\n  |1000>: -0.200127378260643 + -0.193173901701134i\n  |1001>: -0.207177026149653 + -0.349012024171839i\n  |1010>: 0.21010776239526 + -0.0503636451043132i\n  |1011>: 0.316651849527798 + -0.130588543688867i\n  |1100>: 0.262224074902836 + 0.101373951626532i\n  |1101>: -0.32800545084881 + -0.217217548295331i\n  |1110>: 0.0363287265077181 + 0.16989053143464i\n  |1111>: 0.00786855656147617 + 0.178972978485647i\n\nAs a Python list: [(0.08383335501230804+0.0946798570225192j), (-0.1443360362081739+0.11730589159942348j), (0.14695618078731032-0.2538935527679617j), (0.0659457445691654+0.06906656408450641j), (0.07029449568878213-0.04816218873630899j), (0.10330039165912472+0.06532760409035668j), (0.08788553513123636+0.02000523761291961j), (0.14910930089184055+0.3154242274598244j), (-0.20012737826064272-0.1931739017011341j), (-0.20717702614965314-0.3490120241718389j), (0.21010776239526022-0.050363645104313196j), (0.316651849527798-0.13058854368886724j), (0.2622240749028361+0.10137395162653218j), (-0.3280054508488104-0.2172175482953307j), (0.03632872650771806+0.16989053143464025j), (0.007868556561476172+0.17897297848564667j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 5 qubits which prepares the following quantum state from |00000>:\n\n  |00000>: -0.102154945911634 + -0.0554003207402092i\n  |00001>: 0.148187313226173 + 0.171340678642202i\n  |00010>: -0.0765046389658187 + 0.0982932279248882i\n  |00011>: -0.00373279528938344 + 0.143738999861476i\n  |00100>: -0.114269810639482 + 0.0627186238878089i\n  |00101>: -0.00439608476279742 + -0.0686006013993804i\n  |00110>: -0.177937527427898 + 0.32773052687915i\n  |00111>: 0.0224398846445609 + 0.17992821988601i\n  |01000>: 0.00449278726670506 + 0.231515563622913i\n  |01001>: -0.0609026748667434 + 0.0142649486104601i\n  |01010>: -0.233900424077459 + -0.00399852920516462i\n  |01011>: -0.0492625734390313 + 0.0350519171169039i\n  |01100>: -0.11291348172692 + 0.000572705453417477i\n  |01101>: 0.194314313874461 + -0.170756068570703i\n  |01110>: -0.0544646397697808 + 0.00459842134179344i\n  |01111>: 0.11176634650455 + -0.0103878496735085i\n  |10000>: -0.188738137838646 + -0.000997566838319746i\n  |10001>: 0.0402364921564406 + -0.0257303082986964i\n  |10010>: -0.051798971389286 + 0.00487047598966188i\n  |10011>: -0.0669822372820331 + -0.225078783890241i\n  |10100>: 0.205942603466704 + 0.223054763004381i\n  |10101>: -0.0649716137536956 + 0.269176518932222i\n  |10110>: 0.125112181080196 + 0.0276591079635751i\n  |10111>: 0.0354672763618824 + -0.0237340230860424i\n  |11000>: -0.229077244045126 + 0.0328605561176264i\n  |11001>: 0.0919034145221192 + -0.0606445295818293i\n  |11010>: 0.0832879920892468 + 0.0127041679850393i\n  |11011>: -0.16009278034311 + 0.187755225750338i\n  |11100>: -0.0464678750995559 + -0.0251949863699159i\n  |11101>: 0.000247838840313329 + 0.0381396781567156i\n  |11110>: -0.0892057828775745 + -0.233967391034312i\n  |11111>: 0.100769643731127 + -0.0236068989801612i\n\nAs a Python list: [(-0.10215494591163443-0.05540032074020916j), (0.14818731322617282+0.1713406786422022j), (-0.07650463896581874+0.09829322792488823j), (-0.0037327952893834366+0.1437389998614757j), (-0.11426981063948216+0.06271862388780891j), (-0.004396084762797419-0.06860060139938044j), (-0.17793752742789776+0.3277305268791501j), (0.022439884644560853+0.17992821988601018j), (0.00449278726670506+0.23151556362291317j), (-0.06090267486674342+0.014264948610460066j), (-0.23390042407745934-0.003998529205164618j), (-0.04926257343903129+0.035051917116903884j), (-0.11291348172691962+0.0005727054534174769j), (0.19431431387446144-0.17075606857070266j), (-0.05446463976978077+0.0045984213417934365j), (0.11176634650454963-0.010387849673508484j), (-0.18873813783864565-0.0009975668383197457j), (0.04023649215644056-0.025730308298696426j), (-0.05179897138928601+0.00487047598966188j), (-0.06698223728203315-0.2250787838902413j), (0.20594260346670437+0.22305476300438093j), (-0.0649716137536956+0.26917651893222244j), (0.1251121810801955+0.027659107963575083j), (0.035467276361882356-0.02373402308604236j), (-0.22907724404512583+0.03286055611762644j), (0.09190341452211924-0.060644529581829316j), (0.08328799208924677+0.012704167985039276j), (-0.1600927803431099+0.1877552257503384j), (-0.04646787509955589-0.02519498636991586j), (0.00024783884031332945+0.038139678156715554j), (-0.08920578287757448-0.23396739103431194j), (0.1007696437311266-0.02360689898016122j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 5 qubits which prepares the following quantum state from |00000>:\n\n  |00000>: 0.146387287463578 + 0.223292412190043i\n  |00001>: 0.0858767551012804 + -0.0905608623173345i\n  |00010>: 0.0178932667461018 + 0.140832046696919i\n  |00011>: 0.222111337381669 + 0.056199143783533i\n  |00100>: 0.0618920300021216 + 0.0371109741159262i\n  |00101>: -0.0892664662336104 + 0.0469869687111406i\n  |00110>: 0.00813640633868457 + 0.117357082790397i\n  |00111>: 0.083039395659982 + 0.0968414902272791i\n  |01000>: 0.0672519642670893 + -0.218749293226901i\n  |01001>: -0.0195802688168777 + -0.054873254494619i\n  |01010>: 0.204397078099398 + 0.0865224759784599i\n  |01011>: 0.0569950593300778 + 0.105012053460713i\n  |01100>: -0.131471204691798 + 0.150556195599428i\n  |01101>: 0.0419598978616998 + -0.0954590331429235i\n  |01110>: 0.0837570053017113 + 0.013971420992921i\n  |01111>: 0.00770594289780358 + 0.0143978934695712i\n  |10000>: -0.0565352068700152 + 0.164181626304219i\n  |10001>: 0.119557070239313 + 0.125334829808441i\n  |10010>: -0.0562145760872754 + 0.0926243502412666i\n  |10011>: -0.14725636482484 + -0.0667722735891231i\n  |10100>: -0.0292117668876466 + -0.0994029297289935i\n  |10101>: -0.0804193888520801 + 0.160771151284627i\n  |10110>: 0.318854218672658 + 0.117767927765099i\n  |10111>: -0.0302667062174215 + -0.0693956310518514i\n  |11000>: 0.154737417092025 + 0.136769509545186i\n  |11001>: 0.36114633234919 + -0.088641017991809i\n  |11010>: -0.0257653643315088 + -0.163054159889721i\n  |11011>: -0.0822207677707783 + -0.0005222377539477i\n  |11100>: -0.0485997455446401 + 0.086395594556561i\n  |11101>: 0.000594714360814671 + -0.115887857415338i\n  |11110>: 0.0477307966887736 + -0.15062122977193i\n  |11111>: 0.224199506330211 + -0.203949952889304i\n\nAs a Python list: [(0.14638728746357832+0.22329241219004292j), (0.08587675510128039-0.09056086231733453j), (0.01789326674610176+0.14083204669691893j), (0.22211133738166947+0.05619914378353304j), (0.06189203000212159+0.03711097411592618j), (-0.08926646623361041+0.04698696871114062j), (0.008136406338684569+0.11735708279039704j), (0.08303939565998199+0.09684149022727914j), (0.06725196426708935-0.21874929322690098j), (-0.019580268816877747-0.05487325449461897j), (0.20439707809939822+0.08652247597845988j), (0.05699505933007782+0.10501205346071328j), (-0.1314712046917985+0.15055619559942832j), (0.04195989786169978-0.0954590331429235j), (0.08375700530171135+0.01397142099292105j), (0.007705942897803577+0.014397893469571158j), (-0.056535206870015196+0.16418162630421854j), (0.11955707023931296+0.1253348298084411j), (-0.05621457608727539+0.09262435024126663j), (-0.14725636482483964-0.06677227358912313j), (-0.029211766887646564-0.09940292972899349j), (-0.08041938885208008+0.16077115128462696j), (0.31885421867265795+0.11776792776509948j), (-0.03026670621742154-0.0693956310518514j), (0.15473741709202452+0.13676950954518563j), (0.3611463323491904-0.08864101799180897j), (-0.025765364331508826-0.1630541598897207j), (-0.0822207677707783-0.0005222377539477004j), (-0.048599745544640055+0.08639559455656101j), (0.0005947143608146711-0.11588785741533762j), (0.047730796688773634-0.15062122977193035j), (0.224199506330211-0.20394995288930357j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 5 qubits which prepares the following quantum state from |00000>:\n\n  |00000>: -0.15964475037945 + -0.022382369922606i\n  |00001>: -0.098791145665098 + 0.282996362211857i\n  |00010>: 0.0723957606838339 + 0.019951178498933i\n  |00011>: -0.0529907308965836 + 0.109264763443543i\n  |00100>: -0.170471788801531 + -0.095735441015139i\n  |00101>: -0.134165858448449 + 0.340500878361354i\n  |00110>: 0.0199922376933826 + -0.100138770083722i\n  |00111>: 0.0260743068679112 + -0.0350820215550598i\n  |01000>: -0.0858824691074399 + 0.00858349134090695i\n  |01001>: -0.0420379104298173 + 0.119515031050153i\n  |01010>: 0.00446666882616546 + 0.157489498556978i\n  |01011>: 0.0211282694042964 + 0.0177003939189408i\n  |01100>: 0.0476732390213746 + 0.0281268757021322i\n  |01101>: 0.0219612325558809 + -0.0718708121027497i\n  |01110>: -0.000743906500752231 + 0.0443712818396827i\n  |01111>: -0.035437813871179 + -0.258191857542957i\n  |10000>: -0.176003467097391 + -0.208177397360106i\n  |10001>: 0.0310586254662768 + -0.00975842471598805i\n  |10010>: -0.0378354086630671 + 0.0273353571329407i\n  |10011>: 0.253828247851324 + -0.00984568346845946i\n  |10100>: -0.133877152145421 + -0.0408486606980311i\n  |10101>: -0.00427327852457954 + 0.113220938308948i\n  |10110>: -0.0965262613534995 + -0.00469481336066618i\n  |10111>: -0.325065623650845 + -0.058181639749811i\n  |11000>: 0.0493399540711562 + -0.000775322858151805i\n  |11001>: 0.0772906731356175 + 0.129806040282373i\n  |11010>: -0.197085241581419 + 0.297090230294369i\n  |11011>: 0.0847504994438269 + 0.0258972245449681i\n  |11100>: -0.0740849387276466 + -0.0442287594161518i\n  |11101>: 0.00210875835339645 + 0.129907858098261i\n  |11110>: 0.0025890084326658 + 0.0633140929538818i\n  |11111>: 0.256216803748682 + 0.0669820846609969i\n\nAs a Python list: [(-0.15964475037945025-0.022382369922605984j), (-0.09879114566509804+0.2829963622118575j), (0.07239576068383394+0.01995117849893304j), (-0.05299073089658355+0.10926476344354344j), (-0.170471788801531-0.09573544101513905j), (-0.13416585844844872+0.3405008783613543j), (0.0199922376933826-0.10013877008372153j), (0.026074306867911196-0.03508202155505975j), (-0.08588246910743988+0.00858349134090695j), (-0.04203791042981727+0.1195150310501534j), (0.004466668826165459+0.15748949855697766j), (0.02112826940429644+0.017700393918940845j), (0.04767323902137456+0.02812687570213215j), (0.021961232555880852-0.07187081210274968j), (-0.0007439065007522313+0.04437128183968271j), (-0.03543781387117896-0.25819185754295654j), (-0.17600346709739087-0.20817739736010646j), (0.031058625466276808-0.009758424715988048j), (-0.03783540866306712+0.027335357132940736j), (0.2538282478513239-0.00984568346845946j), (-0.13387715214542062-0.04084866069803106j), (-0.004273278524579539+0.11322093830894833j), (-0.09652626135349947-0.004694813360666184j), (-0.32506562365084546-0.058181639749811026j), (0.04933995407115617-0.0007753228581518054j), (0.07729067313561745+0.12980604028237275j), (-0.1970852415814193+0.2970902302943694j), (0.08475049944382693+0.025897224544968123j), (-0.07408493872764663-0.04422875941615183j), (0.002108758353396447+0.12990785809826147j), (0.0025890084326658+0.06331409295388177j), (0.2562168037486819+0.06698208466099691j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 5 qubits which prepares the following quantum state from |00000>:\n\n  |00000>: 0.0229687011872264 + -0.173837073658034i\n  |00001>: 0.0539352518744922 + 0.0642920396694201i\n  |00010>: 0.0559130356420891 + -0.00701292402496855i\n  |00011>: 0.211215790755727 + -0.015641540272942i\n  |00100>: 0.0442733714426346 + 0.00762964022652159i\n  |00101>: -0.0829139950984518 + 0.0179153382482336i\n  |00110>: 0.0412427260645352 + 0.103184266341176i\n  |00111>: -0.00565080301340832 + 0.158767932763442i\n  |01000>: -0.0589131225700474 + -0.182415158824569i\n  |01001>: -0.0636629750032483 + 0.194686365167672i\n  |01010>: -0.0487095568623622 + -0.0404117493183244i\n  |01011>: 0.315407167997404 + 0.125359387221482i\n  |01100>: -0.019499122862616 + 0.0150689471309547i\n  |01101>: 0.0345959063033985 + 0.0142460106509846i\n  |01110>: 0.265131895055445 + 0.0374640896878951i\n  |01111>: 0.036839917542371 + 0.138273473410423i\n  |10000>: 0.00459382111565095 + -0.0556676990189535i\n  |10001>: -0.00601542345584116 + 0.0667623356706844i\n  |10010>: 0.252126728960981 + 0.116914714781563i\n  |10011>: -0.0510274839892653 + 0.0882408266109992i\n  |10100>: 0.113103629019993 + 0.327759547207975i\n  |10101>: -0.184866129180561 + 0.0970344086188258i\n  |10110>: -0.0249803695362445 + -0.0417407552876168i\n  |10111>: 0.0671511486390062 + -0.175881374244521i\n  |11000>: 0.0117019222991781 + 0.0405934500313842i\n  |11001>: -0.141094666066439 + -0.00520067108129749i\n  |11010>: 0.187344173866457 + 0.0438074347410903i\n  |11011>: 0.129426542902018 + -0.101280381543511i\n  |11100>: -0.137649848449775 + -0.124942092948341i\n  |11101>: -0.0645590099376877 + 0.200914668546445i\n  |11110>: -0.222984415007793 + 0.175698312151463i\n  |11111>: 0.178972765909636 + 0.0311323529486942i\n\nAs a Python list: [(0.02296870118722638-0.1738370736580338j), (0.05393525187449217+0.06429203966942007j), (0.05591303564208913-0.0070129240249685474j), (0.21121579075572747-0.01564154027294199j), (0.04427337144263458+0.007629640226521591j), (-0.0829139950984518+0.017915338248233638j), (0.041242726064535225+0.10318426634117633j), (-0.005650803013408324+0.15876793276344178j), (-0.05891312257004738-0.1824151588245687j), (-0.06366297500324831+0.1946863651676725j), (-0.04870955686236217-0.04041174931832441j), (0.3154071679974036+0.12535938722148213j), (-0.019499122862616035+0.01506894713095465j), (0.034595906303398476+0.014246010650984572j), (0.2651318950554451+0.03746408968789506j), (0.03683991754237102+0.13827347341042318j), (0.00459382111565095-0.05566769901895352j), (-0.006015423455841157+0.06676233567068443j), (0.25212672896098076+0.11691471478156272j), (-0.05102748398926528+0.08824082661099919j), (0.11310362901999343+0.3277595472079751j), (-0.1848661291805605+0.09703440861882581j), (-0.02498036953624446-0.041740755287616796j), (0.0671511486390062-0.17588137424452105j), (0.011701922299178064+0.04059345003138421j), (-0.14109466606643925-0.00520067108129749j), (0.1873441738664566+0.04380743474109029j), (0.12942654290201752-0.10128038154351149j), (-0.137649848449775-0.1249420929483412j), (-0.06455900993768769+0.20091466854644507j), (-0.22298441500779317+0.17569831215146287j), (0.17897276590963584+0.031132352948694188j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 5 qubits which prepares the following quantum state from |00000>:\n\n  |00000>: -0.101534947492614 + -0.149350345111902i\n  |00001>: 0.0102133544140058 + -0.00567761575847423i\n  |00010>: 0.0641481183737237 + -0.0966749039714853i\n  |00011>: -0.0477071370579328 + -0.0867447991267452i\n  |00100>: -0.186514046737139 + 0.0763677049511994i\n  |00101>: -0.217499473028104 + -0.25860633910748i\n  |00110>: 0.203040894676693 + -0.0330258254542446i\n  |00111>: -0.154828702411546 + -0.240235857829719i\n  |01000>: -0.0582191077749116 + -0.105715981498644i\n  |01001>: 0.0312098882236476 + 0.023289021484969i\n  |01010>: 0.279983994124102 + 0.191289663332217i\n  |01011>: -0.0502951330910801 + 0.153420446558633i\n  |01100>: 0.0194839251634456 + -0.00567300087334066i\n  |01101>: -0.00798901005965603 + 0.000430546138998751i\n  |01110>: 0.248264142395247 + -0.0354682595966584i\n  |01111>: 0.0765087081477661 + 0.201125335751214i\n  |10000>: 0.248966486343023 + 0.0427137372829804i\n  |10001>: 0.082982583117901 + -0.0322774358347489i\n  |10010>: -0.0192725604989407 + 0.0496892260181972i\n  |10011>: 0.00610995857629984 + -0.118134519376087i\n  |10100>: -0.161607612170857 + -0.0019381133948531i\n  |10101>: 0.0343682240765816 + -0.116463042505317i\n  |10110>: 0.120280388848171 + -0.0746022268454758i\n  |10111>: 0.049685789583697 + -0.0275085242589658i\n  |11000>: -0.0417579334912549 + 0.158914101852676i\n  |11001>: 0.113756507616735 + -0.0618210673989886i\n  |11010>: 0.0107345346900652 + -0.13928525289052i\n  |11011>: 0.120245382808631 + 0.191894323108734i\n  |11100>: -0.0580926173183285 + 0.0434497236557874i\n  |11101>: -0.0340319087814297 + 0.0188549489796896i\n  |11110>: -0.0431711411772757 + 0.101428346715497i\n  |11111>: -0.133411830388395 + 0.307243220102246i\n\nAs a Python list: [(-0.10153494749261371-0.14935034511190212j), (0.010213354414005846-0.005677615758474231j), (0.06414811837372367-0.09667490397148527j), (-0.04770713705793275-0.08674479912674517j), (-0.1865140467371393+0.0763677049511994j), (-0.2174994730281041-0.2586063391074802j), (0.20304089467669328-0.03302582545424459j), (-0.15482870241154617-0.24023585782971862j), (-0.05821910777491159-0.10571598149864433j), (0.03120988822364758+0.02328902148496901j), (0.279983994124102+0.19128966333221678j), (-0.05029513309108012+0.15342044655863263j), (0.01948392516344563-0.005673000873340665j), (-0.007989010059656033+0.0004305461389987509j), (0.24826414239524694-0.0354682595966584j), (0.07650870814776607+0.20112533575121355j), (0.24896648634302324+0.04271373728298043j), (0.08298258311790102-0.03227743583474887j), (-0.019272560498940654+0.04968922601819719j), (0.006109958576299842-0.11813451937608684j), (-0.16160761217085706-0.0019381133948531044j), (0.034368224076581556-0.11646304250531682j), (0.12028038884817072-0.07460222684547584j), (0.04968578958369704-0.027508524258965772j), (-0.04175793349125487+0.15891410185267638j), (0.11375650761673452-0.06182106739898863j), (0.010734534690065222-0.13928525289052024j), (0.1202453828086314+0.19189432310873425j), (-0.05809261731832853+0.04344972365578743j), (-0.03403190878142975+0.018854948979689576j), (-0.043171141177275676+0.1014283467154969j), (-0.13341183038839516+0.30724322010224636j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 6 qubits which prepares the following quantum state from |000000>:\n\n  |000000>: 0.061835637016586 + -0.0180046004972971i\n  |000001>: 0.0606547899537406 + -0.0545056437413137i\n  |000010>: -0.00623368980077135 + 0.0928742871449291i\n  |000011>: 0.00944982549776899 + -0.164566275136035i\n  |000100>: 0.213902858928162 + -0.0518507885092142i\n  |000101>: -0.0993162442616193 + -0.167443562576129i\n  |000110>: 0.0862206361374942 + -0.158706043655266i\n  |000111>: -0.0880431053889425 + 0.0941344472243848i\n  |001000>: -0.0980763948080506 + -0.124543775070411i\n  |001001>: -0.0545402086367485 + 0.0666999762200907i\n  |001010>: -0.0139469574860422 + -0.111088794082675i\n  |001011>: -0.0250996344664744 + -0.00536544007390715i\n  |001100>: -0.142425844062147 + 0.16138714567105i\n  |001101>: -0.140683175248258 + -0.0378906101502481i\n  |001110>: 0.0724630717761167 + 0.0569005692460121i\n  |001111>: 0.0493236201281415 + 0.0745230214433225i\n  |010000>: 0.0251730051152354 + 0.0217479219568765i\n  |010001>: 0.0399860012885919 + 0.0318306479855284i\n  |010010>: -0.090094928797687 + 0.000572711181623538i\n  |010011>: 0.0717129510917072 + 0.0168219489862503i\n  |010100>: -0.0244426928874828 + -0.110569603222142i\n  |010101>: -0.0379118498872249 + -0.0812006685269115i\n  |010110>: 0.015402687041967 + -0.0181900271170342i\n  |010111>: -0.0363903457377718 + 0.0518700019589014i\n  |011000>: 0.218053625603318 + 0.0383891191627815i\n  |011001>: 0.129124963270798 + 0.0463526710970687i\n  |011010>: -0.0331577119490295 + -0.0725784790800827i\n  |011011>: 0.0868201143531845 + 0.102804113193945i\n  |011100>: 0.0927296080038192 + -0.130826720090862i\n  |011101>: -0.183898045278535 + -0.0607274155697218i\n  |011110>: 0.148194867884809 + -0.0163797169306704i\n  |011111>: -0.0303944560581389 + 0.0698825155665998i\n  |100000>: 0.0264586866975571 + 0.0177757571090814i\n  |100001>: 0.00733273741379155 + 0.0289342905939217i\n  |100010>: 0.042934220872713 + -0.0607979374855742i\n  |100011>: 0.053893527000532 + -0.12197595498486i\n  |100100>: -0.0811402805916564 + -0.0270448713903596i\n  |100101>: -0.0161463864656617 + -0.0992389204217067i\n  |100110>: -0.138787717577003 + -0.0721114924429147i\n  |100111>: -0.134391684292919 + -0.0202980170433384i\n  |101000>: -0.0111294718619702 + -0.149879173946182i\n  |101001>: 0.0369729791155961 + 0.0604968873088034i\n  |101010>: -0.0552776635939706 + -0.0473601627560346i\n  |101011>: -0.176390787050111 + 0.0475124254116766i\n  |101100>: 0.220467185650564 + -0.0774904876441132i\n  |101101>: -0.06070950166469 + 0.155354344334611i\n  |101110>: 0.0396989961759711 + -0.079572496330871i\n  |101111>: -0.0850763794195493 + 0.000481240840021682i\n  |110000>: 0.0322370076914952 + -0.00293262198841171i\n  |110001>: -0.0113541261251219 + 0.104261190400828i\n  |110010>: -0.0176985353059743 + 0.0684640426095818i\n  |110011>: -0.178899414521723 + 0.0878179595394861i\n  |110100>: 0.0964316142885627 + -0.0989642697067095i\n  |110101>: -0.0712168618862257 + 0.0153405950281047i\n  |110110>: 0.0483818243046475 + 0.0712039188330833i\n  |110111>: 0.027580490814855 + 0.104933723599535i\n  |111000>: -0.0837076124454188 + 0.096806385789998i\n  |111001>: -0.0110066849636747 + 0.160146083991072i\n  |111010>: -0.13641246403578 + 0.144149333546188i\n  |111011>: -0.054227467633946 + -0.0945522990212301i\n  |111100>: -0.0272269893481073 + -0.0751544506642745i\n  |111101>: -0.00865409459075684 + -0.0570574403160865i\n  |111110>: -0.0739098759640263 + 0.0316561895701652i\n  |111111>: -0.0262425323550656 + -0.0405956119970396i\n\nAs a Python list: [(0.06183563701658601-0.01800460049729706j), (0.06065478995374061-0.05450564374131371j), (-0.006233689800771353+0.09287428714492914j), (0.00944982549776899-0.164566275136035j), (0.21390285892816197-0.051850788509214187j), (-0.09931624426161927-0.16744356257612944j), (0.08622063613749421-0.15870604365526644j), (-0.08804310538894247+0.09413444722438477j), (-0.09807639480805064-0.12454377507041123j), (-0.05454020863674848+0.06669997622009069j), (-0.013946957486042199-0.11108879408267465j), (-0.02509963446647437-0.005365440073907153j), (-0.14242584406214737+0.1613871456710504j), (-0.14068317524825813-0.03789061015024808j), (0.07246307177611672+0.056900569246012084j), (0.04932362012814153+0.07452302144332248j), (0.025173005115235444+0.021747921956876477j), (0.03998600128859186+0.0318306479855284j), (-0.09009492879768702+0.0005727111816235376j), (0.07171295109170718+0.016821948986250272j), (-0.024442692887482822-0.11056960322214206j), (-0.03791184988722487-0.0812006685269115j), (0.015402687041967027-0.01819002711703417j), (-0.03639034573777185+0.051870001958901436j), (0.21805362560331792+0.038389119162781475j), (0.1291249632707979+0.04635267109706875j), (-0.03315771194902947-0.07257847908008275j), (0.08682011435318454+0.1028041131939447j), (0.09272960800381917-0.13082672009086224j), (-0.18389804527853476-0.06072741556972177j), (0.14819486788480868-0.0163797169306704j), (-0.030394456058138942+0.06988251556659979j), (0.026458686697557094+0.017775757109081355j), (0.007332737413791555+0.02893429059392172j), (0.04293422087271305-0.06079793748557418j), (0.05389352700053201-0.1219759549848605j), (-0.08114028059165637-0.02704487139035956j), (-0.01614638646566172-0.09923892042170666j), (-0.13878771757700264-0.07211149244291472j), (-0.1343916842929193-0.020298017043338352j), (-0.011129471861970183-0.1498791739461823j), (0.03697297911559611+0.06049688730880342j), (-0.05527766359397065-0.04736016275603465j), (-0.1763907870501114+0.04751242541167656j), (0.2204671856505644-0.07749048764411319j), (-0.06070950166469002+0.15535434433461143j), (0.0396989961759711-0.07957249633087099j), (-0.08507637941954925+0.00048124084002168185j), (0.03223700769149515-0.002932621988411712j), (-0.011354126125121898+0.10426119040082837j), (-0.017698535305974344+0.06846404260958182j), (-0.1788994145217228+0.08781795953948612j), (0.09643161428856269-0.09896426970670953j), (-0.07121686188622565+0.01534059502810466j), (0.04838182430464749+0.07120391883308334j), (0.027580490814854988+0.1049337235995353j), (-0.0837076124454188+0.09680638578999802j), (-0.011006684963674683+0.16014608399107186j), (-0.13641246403578045+0.14414933354618809j), (-0.054227467633945974-0.09455229902123012j), (-0.027226989348107297-0.07515445066427445j), (-0.008654094590756844-0.05705744031608647j), (-0.07390987596402626+0.03165618957016523j), (-0.026242532355065573-0.04059561199703956j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 6 qubits which prepares the following quantum state from |000000>:\n\n  |000000>: 0.0612282087531191 + 0.045153059828503i\n  |000001>: 0.0480884600601565 + 0.108386616633217i\n  |000010>: -0.042307173998394 + 0.0575786866892797i\n  |000011>: 0.170749944632644 + 0.0724266643435543i\n  |000100>: -0.112084933394741 + -0.0271564680073516i\n  |000101>: -0.0105618538731673 + 0.00332763119647713i\n  |000110>: -0.00920557143631452 + 0.0231402206009956i\n  |000111>: -0.00626171696393372 + -0.0277529777218753i\n  |001000>: -0.0110970608936088 + 0.0111874253652535i\n  |001001>: -0.102527238629022 + -0.0515683540370713i\n  |001010>: -0.130699815789341 + 0.00341521947424624i\n  |001011>: 0.12982869225476 + -0.0466690410937184i\n  |001100>: 0.110193948277781 + -0.0769074520727955i\n  |001101>: -0.0806993849770375 + 0.165196775792083i\n  |001110>: 0.177033479111246 + 0.105042338354758i\n  |001111>: 0.00235848222889082 + 0.0021906733205575i\n  |010000>: -0.0152504088969691 + 0.0129582155224071i\n  |010001>: -0.0320002303762957 + -0.141520713868605i\n  |010010>: 0.150392573424645 + -0.0114550629040309i\n  |010011>: 0.0758003266741443 + 0.101230847876625i\n  |010100>: -0.064813517654507 + -0.111932532559858i\n  |010101>: 0.107981260155299 + 0.293892798065649i\n  |010110>: 0.0835455243908696 + 0.044169020561078i\n  |010111>: -0.00705051317991699 + 0.158620587517251i\n  |011000>: -0.0954980582802383 + -0.0696123072389292i\n  |011001>: 0.045431403284664 + 0.0131967091407138i\n  |011010>: 0.0494579581077662 + -0.101235484162833i\n  |011011>: -0.0153347597285496 + 0.0255558193706032i\n  |011100>: -0.0178558982363147 + 0.0576127570542548i\n  |011101>: 0.0503392849896302 + 0.136928391556743i\n  |011110>: -0.0236699612961021 + -0.0589175774972701i\n  |011111>: 0.060807165968299 + 0.0284473759907759i\n  |100000>: -0.0607624220111405 + -0.148397708279372i\n  |100001>: 0.0512721369065745 + -0.0716071033361014i\n  |100010>: 0.106704562528955 + 0.121723340895208i\n  |100011>: 0.116668759433818 + 0.0282503526042834i\n  |100100>: -0.0754861979967804 + -0.0345245412100061i\n  |100101>: -0.0236200177609254 + -0.148889947949228i\n  |100110>: 0.0938327611444863 + 0.00402826053786138i\n  |100111>: -0.0020227108712541 + -0.0107917769201888i\n  |101000>: 0.148010073444601 + 0.0707524460670192i\n  |101001>: -0.0183407989544064 + 0.016900727949731i\n  |101010>: 0.0284158881396195 + 0.0482185486823243i\n  |101011>: 0.0190206750463941 + 0.0548578312317664i\n  |101100>: 0.0287031370642866 + -0.00881923770017372i\n  |101101>: 0.0381458726941627 + 0.00381262053775141i\n  |101110>: -0.106166090728057 + -0.0816096031213217i\n  |101111>: 0.123943590486343 + -0.0664842566021396i\n  |110000>: 0.0681615138775226 + -0.130431399968327i\n  |110001>: -0.0584107840905974 + -0.180966386947382i\n  |110010>: -0.00323635256000426 + 0.0404129447339468i\n  |110011>: -0.00264489665804299 + 0.0616775855563509i\n  |110100>: -0.0718452309637043 + -0.152761933501273i\n  |110101>: 0.0307383148797155 + -0.0712166764752828i\n  |110110>: 0.24231557474104 + -0.0348303088667582i\n  |110111>: -0.0251068612927593 + 0.0306643498469016i\n  |111000>: 0.0745540412143835 + -0.231862950927919i\n  |111001>: 0.109667875748741 + 0.0749679407649769i\n  |111010>: 0.0810498250495306 + -0.0977096549684941i\n  |111011>: 0.0407566516973207 + 0.0272539521349763i\n  |111100>: -0.12327467033251 + -0.118912426604644i\n  |111101>: 0.105706147306681 + 0.0600515120174099i\n  |111110>: -0.00786431356691762 + -0.0548713605106805i\n  |111111>: -0.143170317876017 + -0.0207312175848147i\n\nAs a Python list: [(0.06122820875311907+0.04515305982850303j), (0.04808846006015653+0.10838661663321666j), (-0.042307173998394+0.05757868668927969j), (0.17074994463264428+0.07242666434355428j), (-0.11208493339474122-0.027156468007351612j), (-0.010561853873167267+0.0033276311964771264j), (-0.009205571436314517+0.023140220600995645j), (-0.006261716963933724-0.02775297772187533j), (-0.011097060893608762+0.011187425365253507j), (-0.10252723862902197-0.05156835403707125j), (-0.1306998157893407+0.0034152194742462366j), (0.12982869225475954-0.04666904109371836j), (0.1101939482777812-0.07690745207279553j), (-0.08069938497703752+0.16519677579208256j), (0.1770334791112455+0.10504233835475792j), (0.0023584822288908176+0.002190673320557503j), (-0.015250408896969056+0.012958215522407144j), (-0.03200023037629565-0.1415207138686046j), (0.15039257342464493-0.011455062904030896j), (0.07580032667414431+0.10123084787662467j), (-0.06481351765450702-0.11193253255985824j), (0.10798126015529949+0.2938927980656491j), (0.08354552439086961+0.044169020561077965j), (-0.007050513179916988+0.1586205875172513j), (-0.09549805828023832-0.0696123072389292j), (0.04543140328466401+0.013196709140713785j), (0.0494579581077662-0.10123548416283264j), (-0.015334759728549648+0.025555819370603156j), (-0.017855898236314723+0.0576127570542548j), (0.05033928498963022+0.13692839155674266j), (-0.02366996129610211-0.05891757749727013j), (0.060807165968299035+0.028447375990775882j), (-0.060762422011140516-0.14839770827937243j), (0.05127213690657448-0.0716071033361014j), (0.1067045625289547+0.12172334089520818j), (0.11666875943381759+0.02825035260428341j), (-0.07548619799678044-0.03452454121000613j), (-0.0236200177609254-0.14888994794922816j), (0.09383276114448628+0.0040282605378613775j), (-0.002022710871254104-0.01079177692018879j), (0.14801007344460143+0.07075244606701918j), (-0.018340798954406372+0.016900727949730958j), (0.02841588813961955+0.04821854868232428j), (0.01902067504639415+0.05485783123176645j), (0.028703137064286625-0.00881923770017372j), (0.0381458726941627+0.0038126205377514086j), (-0.1061660907280569-0.0816096031213217j), (0.1239435904863431-0.06648425660213965j), (0.06816151387752256-0.13043139996832678j), (-0.058410784090597447-0.18096638694738212j), (-0.003236352560004259+0.04041294473394679j), (-0.0026448966580429876+0.061677585556350945j), (-0.07184523096370429-0.15276193350127326j), (0.030738314879715487-0.07121667647528285j), (0.24231557474103982-0.03483030886675821j), (-0.02510686129275934+0.03066434984690161j), (0.0745540412143835-0.23186295092791884j), (0.10966787574874148+0.07496794076497691j), (0.08104982504953058-0.09770965496849408j), (0.04075665169732075+0.02725395213497626j), (-0.12327467033250993-0.11891242660464424j), (0.10570614730668097+0.06005151201740991j), (-0.007864313566917617-0.054871360510680464j), (-0.14317031787601717-0.020731217584814745j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 6 qubits which prepares the following quantum state from |000000>:\n\n  |000000>: 0.0452523152403199 + -0.0301263595263067i\n  |000001>: -0.11288744460371 + -0.100391728863269i\n  |000010>: -0.0641444263224133 + -0.00516151805916488i\n  |000011>: 0.00308922496009254 + 0.137434718052363i\n  |000100>: -0.0130034311645428 + 0.0171458209543376i\n  |000101>: -0.00465500717835303 + -0.018987003456473i\n  |000110>: 0.0327797864648691 + 0.126555165956491i\n  |000111>: 0.019079309131606 + -0.049510327803945i\n  |001000>: 0.134388866284628 + 0.197625371100801i\n  |001001>: -0.0702729344662775 + -0.0552667447288364i\n  |001010>: 0.0231079107436262 + 0.059348658800832i\n  |001011>: -0.0198021052119566 + -0.0312617762927752i\n  |001100>: -0.0579856304508163 + -0.0708210422262882i\n  |001101>: 0.0242703853196123 + -0.0122278522961982i\n  |001110>: 0.062358768489645 + -0.158555695812347i\n  |001111>: -0.136192471319864 + -0.0196355396293504i\n  |010000>: -0.11084812552077 + 0.158433737869547i\n  |010001>: -0.0960198371816861 + -0.133477770622255i\n  |010010>: -0.129107272402128 + 0.0907414509547083i\n  |010011>: 0.0331173209216634 + -0.0595705975479004i\n  |010100>: -0.105978739113302 + -0.00792999251092469i\n  |010101>: -0.0652448429916488 + 0.0392524649287142i\n  |010110>: -0.233000734833899 + 0.101810888901066i\n  |010111>: 0.107112389922203 + -0.0432244295653192i\n  |011000>: 0.0534379929416336 + -0.0166295591298664i\n  |011001>: 0.0140761292542176 + -0.0424938939790897i\n  |011010>: 0.0154805729958336 + 0.0473292144761059i\n  |011011>: -0.107788438735492 + 0.0168766458516369i\n  |011100>: -0.0394890827270619 + 0.0988446069875104i\n  |011101>: -0.000341324463423625 + 0.118982834990717i\n  |011110>: 0.167375862598242 + -0.02077791900842i\n  |011111>: 0.0132033571581102 + -0.0664185482652909i\n  |100000>: -0.0255526840112293 + -0.0137952199590051i\n  |100001>: 0.176889376646055 + -0.0485308937982695i\n  |100010>: 0.0812886587387778 + -0.105729839124134i\n  |100011>: -0.0699637349980354 + 0.0846065364806209i\n  |100100>: 0.0713208243522895 + 0.0029872098960391i\n  |100101>: -0.0105129284094215 + -0.0639373812493866i\n  |100110>: 0.0293494045243166 + 0.0903216752399094i\n  |100111>: -0.113391932125819 + 0.0988504311673139i\n  |101000>: -0.106656144374658 + 0.151377978965126i\n  |101001>: 0.0264426985838607 + 0.0746958294496771i\n  |101010>: 0.100957470490334 + 0.0367843078227815i\n  |101011>: 0.27170084473249 + 0.0289287767685122i\n  |101100>: 0.250624313326261 + -0.0186753866245193i\n  |101101>: 0.0962502669735251 + -0.0461126446804201i\n  |101110>: 0.0645066175231676 + 0.124136558978693i\n  |101111>: -0.0930486139053243 + 0.00771100869043648i\n  |110000>: -0.0658988769876752 + -0.0619048741503176i\n  |110001>: 0.0477657592532872 + 0.0129298698762892i\n  |110010>: -0.125108824783149 + 0.0433161889509332i\n  |110011>: 0.0231090439522842 + 0.00919541283938911i\n  |110100>: 0.0181829628146151 + 0.195102573555374i\n  |110101>: -0.123217554749136 + 0.0487052923050283i\n  |110110>: 0.00176607536283828 + -0.0399538339295879i\n  |110111>: 0.0594977338916701 + -0.0840501469786492i\n  |111000>: 0.14786906497307 + -0.0753469891048279i\n  |111001>: 0.0303072977712433 + 0.10512667680453i\n  |111010>: -0.0377132846606244 + 0.0199469558567158i\n  |111011>: -0.122087724958449 + 0.122276322340736i\n  |111100>: -0.0534459634220828 + -0.116058218096559i\n  |111101>: 0.0387908475475128 + 0.0223190640515159i\n  |111110>: -0.00595648958906105 + -0.0596574029645103i\n  |111111>: -0.0302123308925621 + 0.099423101690674i\n\nAs a Python list: [(0.04525231524031992-0.030126359526306705j), (-0.11288744460370952-0.10039172886326887j), (-0.06414442632241331-0.005161518059164883j), (0.0030892249600925413+0.13743471805236274j), (-0.013003431164542804+0.017145820954337556j), (-0.004655007178353034-0.01898700345647302j), (0.03277978646486914+0.126555165956491j), (0.01907930913160599-0.04951032780394497j), (0.13438886628462826+0.19762537110080144j), (-0.07027293446627751-0.05526674472883636j), (0.023107910743626236+0.05934865880083201j), (-0.019802105211956602-0.03126177629277523j), (-0.05798563045081632-0.07082104222628818j), (0.02427038531961231-0.012227852296198157j), (0.062358768489644986-0.15855569581234702j), (-0.13619247131986367-0.019635539629350357j), (-0.11084812552076993+0.15843373786954706j), (-0.09601983718168611-0.13347777062225455j), (-0.12910727240212813+0.09074145095470831j), (0.033117320921663446-0.059570597547900395j), (-0.1059787391133019-0.00792999251092469j), (-0.06524484299164876+0.03925246492871419j), (-0.23300073483389916+0.10181088890106646j), (0.10711238992220261-0.043224429565319175j), (0.05343799294163364-0.01662955912986637j), (0.014076129254217563-0.04249389397908973j), (0.015480572995833592+0.047329214476105864j), (-0.10778843873549236+0.016876645851636864j), (-0.0394890827270619+0.09884460698751035j), (-0.00034132446342362505+0.11898283499071707j), (0.16737586259824183-0.020777919008420024j), (0.013203357158110206-0.0664185482652909j), (-0.025552684011229256-0.013795219959005114j), (0.17688937664605522-0.04853089379826947j), (0.0812886587387778-0.10572983912413396j), (-0.06996373499803543+0.08460653648062094j), (0.07132082435228955+0.002987209896039095j), (-0.010512928409421493-0.06393738124938658j), (0.02934940452431663+0.09032167523990939j), (-0.11339193212581898+0.09885043116731392j), (-0.10665614437465777+0.15137797896512636j), (0.026442698583860672+0.0746958294496771j), (0.10095747049033367+0.03678430782278148j), (0.2717008447324899+0.028928776768512236j), (0.25062431332626084-0.018675386624519313j), (0.09625026697352507-0.04611264468042006j), (0.06450661752316758+0.1241365589786933j), (-0.09304861390532435+0.007711008690436478j), (-0.06589887698767524-0.061904874150317604j), (0.04776575925328724+0.012929869876289166j), (-0.1251088247831487+0.043316188950933227j), (0.023109043952284247+0.009195412839389109j), (0.018182962814615112+0.19510257355537425j), (-0.1232175547491363+0.04870529230502829j), (0.001766075362838284-0.03995383392958787j), (0.059497733891670096-0.08405014697864922j), (0.14786906497306987-0.07534698910482794j), (0.030307297771243285+0.10512667680452978j), (-0.03771328466062441+0.019946955856715794j), (-0.12208772495844927+0.12227632234073586j), (-0.05344596342208285-0.11605821809655913j), (0.038790847547512754+0.02231906405151587j), (-0.0059564895890610505-0.059657402964510255j), (-0.03021233089256208+0.09942310169067396j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 6 qubits which prepares the following quantum state from |000000>:\n\n  |000000>: 0.0829041866557441 + -0.052237374286285i\n  |000001>: -0.166270637199488 + -0.0263311719171757i\n  |000010>: -0.0460323346523866 + -0.0159350277182475i\n  |000011>: -0.02728042294519 + -0.17665998013827i\n  |000100>: 0.0943354031218979 + 0.000666349693832349i\n  |000101>: -0.0457355114729771 + 0.0306077461535752i\n  |000110>: 0.0270950247439373 + 0.0402576576721584i\n  |000111>: 0.0785684075953921 + -0.088519141833841i\n  |001000>: -0.145349759203629 + -0.0128996425680127i\n  |001001>: -0.0678950330716193 + -0.0847259870645857i\n  |001010>: 0.0282357651108173 + 0.124547310849649i\n  |001011>: -0.0396283258181405 + 0.0517526299655404i\n  |001100>: 0.0668835336174808 + 0.034019942253158i\n  |001101>: 0.11482609353731 + 0.0303171829012705i\n  |001110>: -0.122683320894332 + -0.0792305188039268i\n  |001111>: -0.112550836826295 + -0.0714774981907294i\n  |010000>: -0.0255063912695271 + -0.0700153761009576i\n  |010001>: -0.0796338312070493 + -0.0280787761081789i\n  |010010>: 0.00999248970969837 + -0.0473707798408491i\n  |010011>: 0.165837453884786 + -0.0740950898227273i\n  |010100>: -0.107139686739082 + 0.14804430249364i\n  |010101>: 0.0118448760900142 + -0.0461010701703896i\n  |010110>: -0.0540631820896013 + -0.0716580020974184i\n  |010111>: -0.0315850550299193 + 0.155775004555186i\n  |011000>: -0.0881702533393875 + 0.132931989597554i\n  |011001>: 0.0705352788319528 + -0.0779195163437865i\n  |011010>: 0.0156478488527249 + 0.0785777770227126i\n  |011011>: -0.00365596526319124 + 0.0926151836813761i\n  |011100>: 0.178151224014536 + -0.0863246824973411i\n  |011101>: 0.163333792838139 + -0.0618075205788041i\n  |011110>: -0.142817344978357 + -0.0929687863398127i\n  |011111>: 0.0188595305632994 + -0.00927062608491894i\n  |100000>: 0.0688954652777101 + 0.059969391916605i\n  |100001>: 0.0120750754975077 + 0.0404563922722613i\n  |100010>: 0.0471758931023566 + 0.09819389300049i\n  |100011>: 0.0513429757711751 + -0.0402767737843889i\n  |100100>: 0.167254357411227 + -0.0984376074683756i\n  |100101>: 0.125347818306987 + -0.00324538806030606i\n  |100110>: 0.0609505811465854 + 0.123172248610437i\n  |100111>: -0.0187312890736605 + 0.0607673580874875i\n  |101000>: -0.101821236553461 + -0.111037125077474i\n  |101001>: 0.0976730201710607 + 0.00178141069540463i\n  |101010>: -0.124041437844253 + -0.0187873800794325i\n  |101011>: 0.0849596500337107 + -0.181194144139231i\n  |101100>: -0.0515143057034453 + 0.000450099380662684i\n  |101101>: -0.0782951055274243 + 0.0603516410427722i\n  |101110>: -0.00971625727329905 + -0.0497927369992635i\n  |101111>: -0.0405546487995921 + 0.0596472552406458i\n  |110000>: 0.0149711640742663 + -0.129079531283682i\n  |110001>: -0.114406389998146 + -0.0243792898065851i\n  |110010>: -0.0978717727102771 + 0.262493382117202i\n  |110011>: 0.0530225235376898 + -0.0629759280471349i\n  |110100>: 0.0521058299046116 + 0.125457852523711i\n  |110101>: -0.0413147923326549 + -0.0163346653981614i\n  |110110>: 0.0360046711317192 + -0.130765454349167i\n  |110111>: -0.00550628125467752 + -0.00515442603642618i\n  |111000>: 0.0419692991779638 + 0.0603801846686957i\n  |111001>: 0.0545631389307315 + 0.0809210234234991i\n  |111010>: 0.16161745254306 + -0.157885816212158i\n  |111011>: 0.102195949782156 + 0.0172513567366687i\n  |111100>: 0.109469087287943 + -0.0950049886318793i\n  |111101>: 0.0592388426829631 + -0.0308919041351081i\n  |111110>: 0.00411321214219021 + -0.218307613367315i\n  |111111>: -0.0503143672501154 + -0.0371326715612904i\n\nAs a Python list: [(0.08290418665574406-0.05223737428628495j), (-0.16627063719948812-0.02633117191717568j), (-0.04603233465238662-0.01593502771824753j), (-0.02728042294519003-0.17665998013826975j), (0.09433540312189793+0.0006663496938323487j), (-0.04573551147297711+0.030607746153575154j), (0.027095024743937306+0.04025765767215837j), (0.07856840759539208-0.08851914183384098j), (-0.14534975920362855-0.012899642568012664j), (-0.06789503307161929-0.08472598706458574j), (0.028235765110817275+0.12454731084964864j), (-0.0396283258181405+0.051752629965540406j), (0.0668835336174808+0.034019942253158034j), (0.11482609353730963+0.030317182901270476j), (-0.12268332089433173-0.07923051880392684j), (-0.11255083682629494-0.0714774981907294j), (-0.02550639126952713-0.07001537610095758j), (-0.07963383120704927-0.0280787761081789j), (0.009992489709698375-0.04737077984084907j), (0.1658374538847861-0.07409508982272732j), (-0.1071396867390821+0.1480443024936395j), (0.011844876090014249-0.04610107017038959j), (-0.054063182089601286-0.07165800209741843j), (-0.03158505502991928+0.15577500455518628j), (-0.08817025333938747+0.13293198959755367j), (0.07053527883195278-0.07791951634378652j), (0.015647848852724897+0.07857777702271262j), (-0.0036559652631912385+0.09261518368137614j), (0.17815122401453604-0.0863246824973411j), (0.16333379283813862-0.061807520578804086j), (-0.14281734497835705-0.09296878633981275j), (0.01885953056329941-0.00927062608491894j), (0.06889546527771011+0.05996939191660496j), (0.01207507549750769+0.04045639227226132j), (0.047175893102356585+0.09819389300049004j), (0.05134297577117508-0.040276773784388896j), (0.1672543574112267-0.09843760746837557j), (0.12534781830698707-0.0032453880603060554j), (0.060950581146585414+0.12317224861043659j), (-0.018731289073660513+0.06076735808748747j), (-0.10182123655346065-0.11103712507747392j), (0.09767302017106072+0.0017814106954046286j), (-0.12404143784425345-0.01878738007943252j), (0.08495965003371073-0.18119414413923074j), (-0.0515143057034453+0.0004500993806626836j), (-0.07829510552742434+0.06035164104277219j), (-0.00971625727329905-0.04979273699926348j), (-0.04055464879959209+0.05964725524064576j), (0.014971164074266298-0.12907953128368166j), (-0.1144063899981462-0.024379289806585054j), (-0.09787177271027706+0.2624933821172015j), (0.05302252353768979-0.06297592804713491j), (0.05210582990461165+0.12545785252371094j), (-0.04131479233265487-0.01633466539816142j), (0.03600467113171916-0.1307654543491669j), (-0.005506281254677518-0.0051544260364261765j), (0.04196929917796384+0.06038018466869572j), (0.054563138930731454+0.08092102342349906j), (0.16161745254305984-0.1578858162121578j), (0.10219594978215615+0.01725135673666869j), (0.10946908728794276-0.09500498863187934j), (0.059238842682963144-0.030891904135108096j), (0.004113212142190214-0.21830761336731488j), (-0.050314367250115434-0.037132671561290416j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T1", "task_code": "A_stateprep", "task_name": "State Preparation", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "Write a Qiskit function `solve()` that returns a QuantumCircuit on 6 qubits which prepares the following quantum state from |000000>:\n\n  |000000>: 0.0307517047054373 + -0.103762936909031i\n  |000001>: -0.0162193139216204 + -0.0231649064249765i\n  |000010>: -0.0237062796636347 + -0.000324961628490575i\n  |000011>: 0.131778294508062 + -0.0046014370477725i\n  |000100>: 0.0524359999069495 + 0.146527908027365i\n  |000101>: 0.0114609190413422 + -0.0332741781780309i\n  |000110>: -0.0205227890636068 + 0.117095957652473i\n  |000111>: -0.0338036516173928 + 0.0647981236815482i\n  |001000>: -0.0650688814138157 + 0.186667081943993i\n  |001001>: -0.00806665938214324 + 0.0358997612022261i\n  |001010>: -0.0936826347813809 + -0.0859594111290518i\n  |001011>: -0.124431952879759 + 0.0904540552693738i\n  |001100>: -0.0568594396111664 + -0.0600040111700858i\n  |001101>: 0.00372924814166591 + -0.0850496322548099i\n  |001110>: -0.0429943858072483 + 0.0568712915251109i\n  |001111>: 0.0350759007078257 + -0.0715541783604655i\n  |010000>: -0.00925293878860388 + 0.133853914136968i\n  |010001>: -0.028014406078144 + 0.0236804490776713i\n  |010010>: 0.0365072379112856 + -0.027266519891143i\n  |010011>: 0.0410199284312108 + 0.0408722746936016i\n  |010100>: -0.0116490314121095 + -0.257344495747201i\n  |010101>: 0.0199213853546638 + 0.107147481819521i\n  |010110>: -0.0412178759338007 + -0.156964649746103i\n  |010111>: 0.0189739395179524 + 0.205185764660269i\n  |011000>: 0.0610315394552437 + 0.114198147861873i\n  |011001>: -0.0975220072274425 + -0.0927149075557634i\n  |011010>: 0.0820884079099171 + 0.227343411721046i\n  |011011>: -0.0977848904907544 + -0.0456290298784011i\n  |011100>: -0.0746695390368729 + -0.113354486725065i\n  |011101>: 0.0590270638165689 + 0.0777494436122087i\n  |011110>: 0.0277033023234663 + 0.150954213686439i\n  |011111>: -0.0476808138963053 + 0.000160469880774312i\n  |100000>: -0.0575698897323658 + 0.0222762578483973i\n  |100001>: -0.128918032692532 + -0.0197333651512639i\n  |100010>: 0.072621345886686 + -0.13427791768978i\n  |100011>: -0.070273174302909 + 0.075821240701383i\n  |100100>: 0.0225561176830351 + -0.0405065945929262i\n  |100101>: -0.0329537464461802 + -0.00522558488772212i\n  |100110>: -0.00693064749010797 + -0.1302209100329i\n  |100111>: 0.157868164199663 + 0.142234951209479i\n  |101000>: 0.00447571146112868 + -0.00581034206792739i\n  |101001>: 0.0823131106845987 + -0.0786855351637327i\n  |101010>: 0.102416787791075 + 0.0582728575890081i\n  |101011>: 0.0786012899396401 + -0.0929675128255908i\n  |101100>: 0.0654784676518278 + -0.0713715757599999i\n  |101101>: 0.0539657668193829 + -0.0806239912546566i\n  |101110>: -0.00165626913176817 + -0.0501400558963244i\n  |101111>: -0.130165701489476 + -0.0212000225231125i\n  |110000>: -0.0657316941819656 + -0.0793869944324586i\n  |110001>: -0.127788165025833 + 0.110388090321168i\n  |110010>: 0.00824293679382792 + 0.0491075339481737i\n  |110011>: 0.0196118434650091 + -0.193693044216056i\n  |110100>: -0.0999640453300837 + -0.118406914815018i\n  |110101>: 0.0223017053252034 + 0.00177757292786897i\n  |110110>: 0.0280579477579622 + 0.123883153905985i\n  |110111>: 0.0589950462681272 + -0.0865544795225887i\n  |111000>: -0.0872095440212336 + 0.0790594549541337i\n  |111001>: 0.128694802456896 + 0.144175440339593i\n  |111010>: -0.00525043269863343 + 0.0331515032612402i\n  |111011>: -0.179141223616671 + -0.0545436984971795i\n  |111100>: -0.0337905968407463 + 0.149701316078717i\n  |111101>: -0.135052009900209 + 0.134829829430199i\n  |111110>: 0.0091002890595299 + 0.00947443964458621i\n  |111111>: -0.0370566720351343 + -0.0870408547325987i\n\nAs a Python list: [(0.03075170470543731-0.10376293690903131j), (-0.016219313921620356-0.02316490642497646j), (-0.023706279663634693-0.00032496162849057514j), (0.13177829450806208-0.004601437047772502j), (0.05243599990694948+0.14652790802736473j), (0.011460919041342199-0.03327417817803086j), (-0.020522789063606817+0.1170959576524733j), (-0.03380365161739283+0.06479812368154815j), (-0.06506888141381566+0.1866670819439933j), (-0.008066659382143238+0.03589976120222614j), (-0.09368263478138093-0.0859594111290518j), (-0.124431952879759+0.09045405526937383j), (-0.05685943961116645-0.06000401117008581j), (0.0037292481416659105-0.08504963225480994j), (-0.04299438580724833+0.05687129152511091j), (0.03507590070782573-0.0715541783604655j), (-0.009252938788603877+0.13385391413696823j), (-0.028014406078143962+0.023680449077671258j), (0.036507237911285594-0.027266519891142992j), (0.04101992843121078+0.04087227469360156j), (-0.011649031412109528-0.2573444957472011j), (0.019921385354663756+0.10714748181952088j), (-0.041217875933800725-0.15696464974610333j), (0.01897393951795244+0.20518576466026917j), (0.06103153945524371+0.11419814786187338j), (-0.09752200722744246-0.09271490755576337j), (0.08208840790991706+0.22734341172104613j), (-0.09778489049075435-0.04562902987840113j), (-0.07466953903687286-0.11335448672506537j), (0.05902706381656885+0.07774944361220869j), (0.02770330232346633+0.1509542136864386j), (-0.047680813896305324+0.0001604698807743123j), (-0.05756988973236581+0.022276257848397252j), (-0.12891803269253216-0.019733365151263907j), (0.072621345886686-0.1342779176897802j), (-0.07027317430290904+0.07582124070138305j), (0.022556117683035073-0.04050659459292625j), (-0.032953746446180175-0.005225584887722122j), (-0.006930647490107966-0.13022091003289965j), (0.1578681641996627+0.14223495120947893j), (0.004475711461128679-0.005810342067927387j), (0.08231311068459872-0.07868553516373272j), (0.10241678779107458+0.05827285758900807j), (0.07860128993964012-0.09296751282559079j), (0.06547846765182783-0.07137157575999986j), (0.053965766819382865-0.08062399125465655j), (-0.0016562691317681749-0.05014005589632435j), (-0.1301657014894761-0.021200022523112518j), (-0.06573169418196556-0.0793869944324586j), (-0.12778816502583298+0.11038809032116793j), (0.008242936793827923+0.04910753394817372j), (0.019611843465009146-0.1936930442160557j), (-0.09996404533008371-0.11840691481501774j), (0.022301705325203352+0.0017775729278689694j), (0.028057947757962238+0.12388315390598473j), (0.05899504626812716-0.08655447952258867j), (-0.08720954402123357+0.07905945495413372j), (0.1286948024568965+0.14417544033959265j), (-0.005250432698633434+0.03315150326124021j), (-0.17914122361667134-0.05454369849717952j), (-0.033790596840746326+0.14970131607871726j), (-0.13505200990020866+0.13482982943019942j), (0.009100289059529901+0.009474439644586214j), (-0.037056672035134255-0.08704085473259872j)]\n\nRequirements:\n- Use ONLY elementary gates: rx, ry, rz, h, x, y, z, cx, cz, ccx, swap.\n- Do NOT use initialize(), prepare_state(), or isometry().\n- You must decompose the state preparation into a gate sequence yourself.\n- The circuit should achieve fidelity > 0.999 with the target state.\n- Return ONLY the QuantumCircuit object from solve().\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.5 for the following 2-qubit Hamiltonian:\n\n  H = -0.5455 * XY\n  -0.7873 * IY\n  -0.8996 * ZX\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.5 for the following 2-qubit Hamiltonian:\n\n  H = -1.9675 * ZY\n  +0.5855 * IX\n  +1.5482 * XY\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.5 for the following 2-qubit Hamiltonian:\n\n  H = +0.2541 * XY\n  -0.7526 * XZ\n  -0.5842 * XI\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.5 for the following 2-qubit Hamiltonian:\n\n  H = -0.7869 * XZ\n  -1.0446 * IX\n  -0.5466 * XX\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.5 for the following 2-qubit Hamiltonian:\n\n  H = +0.9388 * XI\n  +0.0713 * XX\n  -0.4503 * XZ\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.8 for the following 2-qubit Hamiltonian:\n\n  H = +0.2743 * YI\n  -0.6541 * XZ\n  +0.2748 * YZ\n  +1.7334 * IX\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.8 for the following 2-qubit Hamiltonian:\n\n  H = +0.7792 * XZ\n  +1.0145 * XI\n  +1.8101 * ZI\n  +1.5772 * XX\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.8 for the following 2-qubit Hamiltonian:\n\n  H = -0.4737 * XX\n  +0.4162 * XZ\n  +0.6416 * XY\n  -0.3768 * ZI\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.8 for the following 2-qubit Hamiltonian:\n\n  H = +1.1815 * XY\n  -1.9782 * ZY\n  +0.8636 * XI\n  +0.4761 * YZ\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=0.8 for the following 2-qubit Hamiltonian:\n\n  H = +0.7994 * IX\n  +0.7193 * ZX\n  -1.4895 * XZ\n  -0.1415 * XY\n\nWrite a function `solve()` that returns a QuantumCircuit on 2 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 3-qubit Hamiltonian:\n\n  H = -1.5967 * ZXX\n  -0.6182 * ZZY\n  -0.1781 * XYY\n  -1.9327 * IIZ\n  -0.1992 * IXI\n\nWrite a function `solve()` that returns a QuantumCircuit on 3 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 3-qubit Hamiltonian:\n\n  H = +0.2257 * ZXZ\n  +0.1715 * ZYX\n  +1.7214 * IYZ\n  -0.8902 * ZYZ\n  +1.4067 * XIX\n\nWrite a function `solve()` that returns a QuantumCircuit on 3 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 3-qubit Hamiltonian:\n\n  H = +0.8308 * IZY\n  -1.3314 * YYI\n  -0.4240 * IXZ\n  +0.0524 * ZYY\n  -0.2056 * IYZ\n\nWrite a function `solve()` that returns a QuantumCircuit on 3 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 3-qubit Hamiltonian:\n\n  H = +0.8654 * IIY\n  +1.2474 * ZYX\n  +0.5024 * YZX\n  +0.5194 * YYZ\n  +1.9143 * IXI\n\nWrite a function `solve()` that returns a QuantumCircuit on 3 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 3-qubit Hamiltonian:\n\n  H = -0.7012 * YXY\n  -1.2414 * ZYX\n  -1.5983 * XXY\n  -1.9748 * XZX\n  +1.6701 * YIX\n\nWrite a function `solve()` that returns a QuantumCircuit on 3 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 4-qubit Hamiltonian:\n\n  H = -0.4390 * YIXI\n  -1.7338 * ZYZI\n  +1.3139 * ZXIZ\n  -1.8077 * XIYZ\n  -0.5276 * XZZI\n  -0.0043 * XIIX\n  -1.2530 * YXIZ\n  +0.5370 * XIII\n\nWrite a function `solve()` that returns a QuantumCircuit on 4 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 4-qubit Hamiltonian:\n\n  H = +1.0933 * ZZXI\n  +1.2545 * IIXZ\n  +1.4708 * YZIZ\n  +0.4937 * YIIZ\n  -1.4802 * XZYX\n  -0.6481 * XXIZ\n  +1.9515 * XXYI\n  +0.0571 * XZZX\n\nWrite a function `solve()` that returns a QuantumCircuit on 4 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 4-qubit Hamiltonian:\n\n  H = +0.3080 * ZZYX\n  +1.2602 * IXXZ\n  +1.9571 * ZZYI\n  -0.0652 * IZIZ\n  +1.8890 * ZXZZ\n  +1.2911 * IZYZ\n  -0.7081 * IXYI\n  +1.7208 * XXIZ\n\nWrite a function `solve()` that returns a QuantumCircuit on 4 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 4-qubit Hamiltonian:\n\n  H = -1.4741 * YXZZ\n  -0.7391 * XYIY\n  +1.9584 * ZIII\n  -1.7273 * IYXY\n  +0.8273 * ZIZY\n  +1.2059 * ZXYI\n  +0.6877 * ZYYZ\n  +1.2216 * ZXZZ\n\nWrite a function `solve()` that returns a QuantumCircuit on 4 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.0 for the following 4-qubit Hamiltonian:\n\n  H = +1.7998 * XYXY\n  +1.9078 * XIIX\n  -0.9091 * YXZY\n  +1.2691 * XXYY\n  +1.4104 * XXYZ\n  -0.8242 * IIIY\n  +0.9939 * IIYZ\n  +0.8809 * IZII\n\nWrite a function `solve()` that returns a QuantumCircuit on 4 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.5 for the following 5-qubit Hamiltonian:\n\n  H = +0.6380 * YZXZI\n  -1.6716 * IYZZZ\n  -0.8167 * YIYXI\n  +0.5845 * YZZZY\n  -1.0041 * IYZIX\n  +1.8014 * ZIIZZ\n  +0.3863 * IZXZI\n  +1.7987 * IXZXX\n  -1.6412 * YIIIX\n  +1.6995 * IXZYZ\n  -0.8667 * IXYIX\n  -1.9701 * YZIYY\n\nWrite a function `solve()` that returns a QuantumCircuit on 5 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.5 for the following 5-qubit Hamiltonian:\n\n  H = +0.5727 * ZZYXI\n  -0.5244 * YYIXY\n  -0.2466 * ZZYYZ\n  -0.3425 * ZIZYX\n  -0.7530 * YXYXZ\n  -0.5336 * IIXXX\n  -0.6795 * IYYXX\n  +0.7467 * YYXZI\n  +1.5718 * ZYXIY\n  -0.8362 * YIZYZ\n  -0.0410 * IXIYZ\n  +1.9916 * IIYIX\n\nWrite a function `solve()` that returns a QuantumCircuit on 5 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.5 for the following 5-qubit Hamiltonian:\n\n  H = -0.8091 * ZXYII\n  +0.6570 * XXZYZ\n  -1.5554 * XXYZI\n  +0.7886 * ZYZXX\n  +1.4090 * ZYIXX\n  +0.7885 * ZIZYI\n  +0.1254 * YYZYX\n  +0.0806 * YZXII\n  +0.9511 * IYXYZ\n  -0.4809 * YIXZY\n  -0.6900 * ZYIZX\n  -0.1144 * IYIZI\n\nWrite a function `solve()` that returns a QuantumCircuit on 5 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.5 for the following 5-qubit Hamiltonian:\n\n  H = +1.8411 * IZIZX\n  +0.0353 * IYIIX\n  +0.3953 * IZIIZ\n  +0.9101 * XZXXZ\n  +0.4953 * ZYYZI\n  -0.2601 * XIYXZ\n  -0.7357 * YZZXY\n  -0.9034 * YXYIX\n  +0.9686 * IIZZZ\n  +0.5952 * YIYYX\n  -1.0141 * XZYZY\n  +0.5506 * XXXII\n\nWrite a function `solve()` that returns a QuantumCircuit on 5 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T2", "task_code": "G1_trotter", "task_name": "Trotterization", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "Construct a Trotter circuit for the time evolution operator e^{-iHt} with t=1.5 for the following 5-qubit Hamiltonian:\n\n  H = +0.9718 * XYZYY\n  +0.1145 * IZIZI\n  +1.7862 * IZZYX\n  -0.4821 * XXZZY\n  -1.3238 * YZZYZ\n  -1.8761 * IYIIY\n  +1.9121 * IYIIZ\n  +0.6688 * YXIIZ\n  +0.4858 * IXXZI\n  +1.1280 * IIIIX\n  +0.6082 * YYYZY\n  -1.7962 * ZZZXX\n\nWrite a function `solve()` that returns a QuantumCircuit on 5 qubits.\nThe circuit should achieve operator fidelity > 0.99 with the exact time evolution.\nYou may use multiple Trotter steps. Use only standard gates (rx, ry, rz, cx, h).\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^2 -> {0,1}:\n\nTruth table:\n  f(00) = 0\n  f(01) = 1\n  f(10) = 0\n  f(11) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 1 are the input register (q[0]=x0, q[1]=x1)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[1]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^2 -> {0,1}:\n\nTruth table:\n  f(00) = 1\n  f(01) = 1\n  f(10) = 0\n  f(11) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 1 are the input register (q[0]=x0, q[1]=x1)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[1]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^2 -> {0,1}:\n\nTruth table:\n  f(00) = 0\n  f(01) = 1\n  f(10) = 0\n  f(11) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 1 are the input register (q[0]=x0, q[1]=x1)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[1]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^2 -> {0,1}:\n\nTruth table:\n  f(00) = 0\n  f(01) = 1\n  f(10) = 0\n  f(11) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 1 are the input register (q[0]=x0, q[1]=x1)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[1]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^2 -> {0,1}:\n\nTruth table:\n  f(00) = 0\n  f(01) = 0\n  f(10) = 0\n  f(11) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 1 are the input register (q[0]=x0, q[1]=x1)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[1]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 1\n  f(001) = 0\n  f(010) = 0\n  f(011) = 1\n  f(100) = 1\n  f(101) = 1\n  f(110) = 0\n  f(111) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 0\n  f(001) = 1\n  f(010) = 0\n  f(011) = 0\n  f(100) = 0\n  f(101) = 1\n  f(110) = 1\n  f(111) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 0\n  f(001) = 0\n  f(010) = 0\n  f(011) = 0\n  f(100) = 0\n  f(101) = 1\n  f(110) = 0\n  f(111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 0\n  f(001) = 1\n  f(010) = 1\n  f(011) = 1\n  f(100) = 0\n  f(101) = 0\n  f(110) = 0\n  f(111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 0\n  f(001) = 0\n  f(010) = 1\n  f(011) = 0\n  f(100) = 0\n  f(101) = 1\n  f(110) = 0\n  f(111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use as many ancilla qubits as needed. All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 1\n  f(001) = 0\n  f(010) = 0\n  f(011) = 1\n  f(100) = 1\n  f(101) = 1\n  f(110) = 0\n  f(111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 1\n  f(001) = 0\n  f(010) = 1\n  f(011) = 1\n  f(100) = 1\n  f(101) = 0\n  f(110) = 0\n  f(111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 0\n  f(001) = 1\n  f(010) = 1\n  f(011) = 1\n  f(100) = 1\n  f(101) = 0\n  f(110) = 0\n  f(111) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 0\n  f(001) = 0\n  f(010) = 1\n  f(011) = 1\n  f(100) = 1\n  f(101) = 0\n  f(110) = 1\n  f(111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^3 -> {0,1}:\n\nTruth table:\n  f(000) = 1\n  f(001) = 0\n  f(010) = 1\n  f(011) = 1\n  f(100) = 1\n  f(101) = 0\n  f(110) = 0\n  f(111) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 2 are the input register (q[0]=x0, q[1]=x1, q[2]=x2)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[2]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 1\n  f(0001) = 0\n  f(0010) = 0\n  f(0011) = 0\n  f(0100) = 1\n  f(0101) = 1\n  f(0110) = 1\n  f(0111) = 0\n  f(1000) = 1\n  f(1001) = 0\n  f(1010) = 0\n  f(1011) = 1\n  f(1100) = 0\n  f(1101) = 0\n  f(1110) = 1\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 1\n  f(0001) = 1\n  f(0010) = 0\n  f(0011) = 0\n  f(0100) = 0\n  f(0101) = 0\n  f(0110) = 0\n  f(0111) = 1\n  f(1000) = 1\n  f(1001) = 1\n  f(1010) = 0\n  f(1011) = 1\n  f(1100) = 1\n  f(1101) = 0\n  f(1110) = 0\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 1\n  f(0001) = 1\n  f(0010) = 1\n  f(0011) = 0\n  f(0100) = 0\n  f(0101) = 0\n  f(0110) = 0\n  f(0111) = 1\n  f(1000) = 1\n  f(1001) = 1\n  f(1010) = 1\n  f(1011) = 0\n  f(1100) = 0\n  f(1101) = 1\n  f(1110) = 0\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 1\n  f(0001) = 0\n  f(0010) = 1\n  f(0011) = 1\n  f(0100) = 0\n  f(0101) = 1\n  f(0110) = 0\n  f(0111) = 1\n  f(1000) = 1\n  f(1001) = 0\n  f(1010) = 0\n  f(1011) = 0\n  f(1100) = 0\n  f(1101) = 1\n  f(1110) = 0\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 0\n  f(0001) = 1\n  f(0010) = 0\n  f(0011) = 1\n  f(0100) = 0\n  f(0101) = 0\n  f(0110) = 0\n  f(0111) = 0\n  f(1000) = 1\n  f(1001) = 0\n  f(1010) = 1\n  f(1011) = 1\n  f(1100) = 0\n  f(1101) = 0\n  f(1110) = 1\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 2 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 1\n  f(0001) = 1\n  f(0010) = 0\n  f(0011) = 1\n  f(0100) = 0\n  f(0101) = 0\n  f(0110) = 1\n  f(0111) = 1\n  f(1000) = 1\n  f(1001) = 1\n  f(1010) = 1\n  f(1011) = 0\n  f(1100) = 1\n  f(1101) = 0\n  f(1110) = 0\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 1 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 1\n  f(0001) = 1\n  f(0010) = 1\n  f(0011) = 0\n  f(0100) = 0\n  f(0101) = 1\n  f(0110) = 1\n  f(0111) = 0\n  f(1000) = 0\n  f(1001) = 1\n  f(1010) = 1\n  f(1011) = 1\n  f(1100) = 1\n  f(1101) = 1\n  f(1110) = 1\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 1 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 1\n  f(0001) = 0\n  f(0010) = 1\n  f(0011) = 0\n  f(0100) = 0\n  f(0101) = 0\n  f(0110) = 0\n  f(0111) = 1\n  f(1000) = 1\n  f(1001) = 1\n  f(1010) = 0\n  f(1011) = 0\n  f(1100) = 1\n  f(1101) = 1\n  f(1110) = 0\n  f(1111) = 1\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 1 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 0\n  f(0001) = 1\n  f(0010) = 0\n  f(0011) = 1\n  f(0100) = 0\n  f(0101) = 0\n  f(0110) = 1\n  f(0111) = 0\n  f(1000) = 0\n  f(1001) = 0\n  f(1010) = 0\n  f(1011) = 1\n  f(1100) = 0\n  f(1101) = 0\n  f(1110) = 1\n  f(1111) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 1 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T3", "task_code": "H1_oracle", "task_name": "Oracle Synthesis", "workflow_stage": "Construct", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "Implement a quantum oracle U_f for the following boolean function f: {0,1}^4 -> {0,1}:\n\nTruth table:\n  f(0000) = 0\n  f(0001) = 1\n  f(0010) = 1\n  f(0011) = 1\n  f(0100) = 1\n  f(0101) = 0\n  f(0110) = 1\n  f(0111) = 0\n  f(1000) = 1\n  f(1001) = 0\n  f(1010) = 0\n  f(1011) = 1\n  f(1100) = 1\n  f(1101) = 1\n  f(1110) = 0\n  f(1111) = 0\n\nThe oracle should act as U_f|x>|y> = |x>|y XOR f(x)>.\n\nYou may use at most 1 ancilla qubit(s). All ancillae must be returned to |0> (clean computation).\n\nWrite a function `solve()` that returns a QuantumCircuit where:\n  - Qubits 0 to 3 are the input register (q[0]=x0, q[1]=x1, q[2]=x2, q[3]=x3)\n  - The last qubit (highest index) is the output (target) qubit\n  - Any qubits in between are ancillae\n  - IMPORTANT: In the truth table, the input string is read as q[3]...q[1]q[0] (q[0] is the LEAST significant bit).\n    Example: f(01) means q[1]=0, q[0]=1.\n\nUse only cx, ccx, and x gates.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "The following 2-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\ns q[0];\nry(6.232383815049195) q[1];\nh q[0];\nt q[1];\nrz(2.5778010088792107) q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00> -> (0.1066-0.3127i)|00> + (0.1066-0.3127i)|01> + (0.6028+0.1660i)|10> + (0.6028+0.1660i)|11>\n  |01> -> (0.3127+0.1066i)|00> + (-0.3127-0.1066i)|01> + (-0.1660+0.6028i)|10> + (0.1660-0.6028i)|11>\n  |10> -> (-0.5436-0.3089i)|00> + (-0.5436-0.3089i)|01> + (-0.1457+0.2965i)|10> + (-0.1457+0.2965i)|11>\n  |11> -> (0.3089-0.5436i)|00> + (-0.3089+0.5436i)|01> + (-0.2965-0.1457i)|10> + (0.2965+0.1457i)|11>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "The following 2-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\ncz q[0],q[1];\ncx q[0],q[1];\ny q[0];\ns q[0];\nz q[0];\ncz q[1],q[0];\ncx q[0],q[1];\ny q[0];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00> -> (0.0000+1.0000i)|01>\n  |01> -> (0.7071+0.7071i)|00>\n  |10> -> (0.0000+1.0000i)|11>\n  |11> -> (0.7071+0.7071i)|10>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "The following 2-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\ns q[0];\nx q[1];\ncx q[1],q[0];\nrx(4.944298725272166) q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00> -> (-0.7842+0.0000i)|01> + (0.0000-0.6205i)|11>\n  |01> -> (0.6205+0.0000i)|00> + (0.0000-0.7842i)|10>\n  |10> -> (-0.7842+0.0000i)|00> + (0.0000-0.6205i)|10>\n  |11> -> (0.6205+0.0000i)|01> + (0.0000-0.7842i)|11>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "The following 2-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nt q[0];\nry(3.5018632378947836) q[0];\ny q[1];\nh q[0];\ncz q[1],q[0];\nh q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00> -> (0.0000+0.6957i)|00> + (0.0000+0.1267i)|01> + (0.0000-0.6957i)|10> + (0.0000-0.1267i)|11>\n  |01> -> (0.0896-0.0896i)|00> + (-0.4919+0.4919i)|01> + (-0.0896+0.0896i)|10> + (0.4919-0.4919i)|11>\n  |10> -> (0.0000-0.6957i)|00> + (0.0000+0.1267i)|01> + (0.0000-0.6957i)|10> + (0.0000+0.1267i)|11>\n  |11> -> (-0.0896+0.0896i)|00> + (-0.4919+0.4919i)|01> + (-0.0896+0.0896i)|10> + (-0.4919+0.4919i)|11>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "The following 2-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nz q[0];\ns q[0];\nz q[0];\nrx(4.027594337564511) q[1];\nrz(3.1507035243578856) q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00> -> (0.4286-0.0020i)|01> + (0.0041-0.9035i)|11>\n  |01> -> (0.0020+0.4286i)|00> + (0.9035+0.0041i)|10>\n  |10> -> (0.0041+0.9035i)|01> + (-0.4286-0.0020i)|11>\n  |11> -> (-0.9035+0.0041i)|00> + (0.0020-0.4286i)|10>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nh q[0];\ny q[2];\nz q[0];\nry(4.567684551169003) q[0];\nh q[0];\nry(1.0450591829488785) q[2];\nrz(3.5929563116952115) q[1];\nrx(3.4324964786593237) q[2];\nh q[2];\ncz q[2],q[0];\nz q[2];\nrx(5.687740598132069) q[2];\nt q[1];\nrx(4.962966954193391) q[2];\ncx q[1],q[0];\nz q[2];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (-0.5560-0.0640i)|000> + (-0.5600+0.1390i)|001> + (-0.1789-0.3039i)|100> + (0.0959-0.4693i)|101>\n  |001> -> (-0.5600+0.1390i)|000> + (0.5560+0.0640i)|001> + (0.0959-0.4693i)|100> + (0.1789+0.3039i)|101>\n  |010> -> (0.3149+0.4835i)|010> + (0.1219+0.5463i)|011> + (-0.4748+0.0633i)|110> + (-0.2285+0.2687i)|111>\n  |011> -> (-0.1219-0.5463i)|010> + (0.3149+0.4835i)|011> + (0.2285-0.2687i)|110> + (-0.4748+0.0633i)|111>\n  |100> -> (0.0138+0.4027i)|000> + (-0.2920-0.3258i)|001> + (0.5489-0.3141i)|100> + (-0.4906+0.0747i)|101>\n  |101> -> (-0.2920-0.3258i)|000> + (-0.0138-0.4027i)|001> + (-0.4906+0.0747i)|100> + (-0.5489+0.3141i)|101>\n  |110> -> (-0.2120+0.3827i)|010> + (0.3759-0.1451i)|011> + (0.2314+0.4390i)|110> + (-0.4767-0.4156i)|111>\n  |111> -> (-0.3759+0.1451i)|010> + (-0.2120+0.3827i)|011> + (0.4767+0.4156i)|110> + (0.2314+0.4390i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncz q[0],q[2];\ncx q[1],q[0];\ns q[0];\ncz q[2],q[1];\nx q[2];\nh q[1];\ns q[1];\nt q[2];\ncx q[1],q[0];\ncx q[0],q[2];\nt q[2];\ncz q[2],q[1];\nt q[0];\ncz q[2],q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (-0.0000+0.7071i)|011> + (-0.7071+0.0000i)|100>\n  |001> -> (0.0000-0.7071i)|001> + (-0.7071+0.0000i)|110>\n  |010> -> (-0.0000+0.7071i)|001> + (-0.7071+0.0000i)|110>\n  |011> -> (-0.0000+0.7071i)|011> + (0.7071-0.0000i)|100>\n  |100> -> (0.7071+0.0000i)|000> + (-0.7071+0.0000i)|111>\n  |101> -> (0.7071+0.0000i)|010> + (0.7071-0.0000i)|101>\n  |110> -> (-0.7071+0.0000i)|010> + (0.7071-0.0000i)|101>\n  |111> -> (0.7071+0.0000i)|000> + (0.7071-0.0000i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ny q[1];\ncz q[1],q[2];\nz q[0];\nh q[1];\ncz q[2],q[0];\ns q[0];\nh q[2];\nh q[1];\ncx q[2],q[1];\nt q[0];\ncz q[2],q[1];\nx q[0];\ncx q[1],q[2];\nh q[0];\ns q[2];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (-0.5000+0.0000i)|100> + (-0.5000+0.0000i)|101> + (-0.5000+0.0000i)|110> + (-0.5000+0.0000i)|111>\n  |001> -> (0.0000+0.5000i)|100> + (0.0000-0.5000i)|101> + (0.0000+0.5000i)|110> + (0.0000-0.5000i)|111>\n  |010> -> (0.0000-0.5000i)|000> + (0.0000-0.5000i)|001> + (0.0000+0.5000i)|010> + (0.0000+0.5000i)|011>\n  |011> -> (-0.5000+0.0000i)|000> + (0.5000+0.0000i)|001> + (0.5000+0.0000i)|010> + (-0.5000+0.0000i)|011>\n  |100> -> (-0.5000+0.0000i)|100> + (-0.5000+0.0000i)|101> + (0.5000+0.0000i)|110> + (0.5000+0.0000i)|111>\n  |101> -> (0.0000-0.5000i)|100> + (0.0000+0.5000i)|101> + (0.0000+0.5000i)|110> + (0.0000-0.5000i)|111>\n  |110> -> (0.0000-0.5000i)|000> + (0.0000-0.5000i)|001> + (0.0000-0.5000i)|010> + (0.0000-0.5000i)|011>\n  |111> -> (0.5000+0.0000i)|000> + (-0.5000+0.0000i)|001> + (0.5000+0.0000i)|010> + (-0.5000+0.0000i)|011>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nry(4.88077357963315) q[1];\ns q[1];\ncx q[0],q[2];\nry(5.198606068864962) q[1];\nry(0.7036137925742918) q[0];\nz q[0];\nrx(0.12030840945657001) q[2];\nt q[0];\nx q[2];\nx q[1];\nt q[1];\nh q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (0.1910-0.1944i)|000> + (-0.1000+0.0009i)|001> + (-0.6568-0.4941i)|010> + (0.0422+0.2987i)|011> + (-0.0891+0.0713i)|100> + (0.0416+0.0046i)|101> + (0.2484+0.2381i)|110> + (-0.0027-0.1263i)|111>\n  |001> -> (0.0327-0.0262i)|000> + (0.1134+0.0126i)|001> + (-0.0912-0.0874i)|010> + (-0.0073-0.3441i)|011> + (-0.0701+0.0714i)|100> + (-0.2725+0.0025i)|101> + (0.2411+0.1814i)|110> + (0.1151+0.8138i)|111>\n  |010> -> (-0.1555+0.8070i)|000> + (0.2499-0.1691i)|001> + (-0.2721-0.0161i)|010> + (0.0665+0.0748i)|011> + (0.1049-0.3278i)|100> + (-0.1123+0.0579i)|101> + (0.1123+0.0202i)|110> + (-0.0239-0.0344i)|111>\n  |011> -> (-0.0385+0.1203i)|000> + (-0.3059+0.1576i)|001> + (-0.0412-0.0074i)|010> + (-0.0651-0.0937i)|011> + (0.0571-0.2962i)|100> + (0.6807-0.4607i)|101> + (0.0999+0.0059i)|110> + (0.1810+0.2037i)|111>\n  |100> -> (-0.0651+0.0937i)|000> + (0.0412-0.0074i)|001> + (0.3059+0.1576i)|010> + (-0.0385-0.1203i)|011> + (-0.1810+0.2037i)|100> + (0.0999-0.0059i)|101> + (0.6807+0.4607i)|110> + (-0.0571-0.2962i)|111>\n  |101> -> (0.0665-0.0748i)|000> + (0.2721-0.0161i)|001> + (-0.2499-0.1691i)|010> + (-0.1555-0.8070i)|011> + (0.0239-0.0344i)|100> + (0.1123-0.0202i)|101> + (-0.1123-0.0579i)|110> + (-0.1049-0.3278i)|111>\n  |110> -> (0.0073-0.3441i)|000> + (-0.0912+0.0874i)|001> + (0.1134-0.0126i)|010> + (-0.0327-0.0262i)|011> + (0.1151-0.8138i)|100> + (-0.2411+0.1814i)|101> + (0.2725+0.0025i)|110> + (-0.0701-0.0714i)|111>\n  |111> -> (-0.0422+0.2987i)|000> + (-0.6568+0.4941i)|001> + (-0.1000-0.0009i)|010> + (-0.1910-0.1944i)|011> + (-0.0027+0.1263i)|100> + (-0.2484+0.2381i)|101> + (-0.0416+0.0046i)|110> + (-0.0891-0.0713i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncx q[2],q[0];\ns q[2];\nh q[1];\nrz(3.504125488335103) q[1];\nz q[2];\nz q[2];\nh q[0];\nz q[1];\ncx q[1],q[0];\ncx q[2],q[0];\nx q[2];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (-0.0692+0.0127i)|000> + (-0.0692+0.0127i)|001> + (-0.0692-0.0127i)|010> + (-0.0692-0.0127i)|011> + (-0.0892-0.4869i)|100> + (-0.0892-0.4869i)|101> + (0.0892-0.4869i)|110> + (0.0892-0.4869i)|111>\n  |001> -> (0.0692-0.0127i)|000> + (-0.0692+0.0127i)|001> + (-0.0692-0.0127i)|010> + (0.0692+0.0127i)|011> + (-0.0892-0.4869i)|100> + (0.0892+0.4869i)|101> + (-0.0892+0.4869i)|110> + (0.0892-0.4869i)|111>\n  |010> -> (-0.0692+0.0127i)|000> + (-0.0692+0.0127i)|001> + (0.0692+0.0127i)|010> + (0.0692+0.0127i)|011> + (-0.0892-0.4869i)|100> + (-0.0892-0.4869i)|101> + (-0.0892+0.4869i)|110> + (-0.0892+0.4869i)|111>\n  |011> -> (0.0692-0.0127i)|000> + (-0.0692+0.0127i)|001> + (0.0692+0.0127i)|010> + (-0.0692-0.0127i)|011> + (-0.0892-0.4869i)|100> + (0.0892+0.4869i)|101> + (0.0892-0.4869i)|110> + (-0.0892+0.4869i)|111>\n  |100> -> (-0.4869+0.0892i)|000> + (0.4869-0.0892i)|001> + (0.4869+0.0892i)|010> + (-0.4869-0.0892i)|011> + (-0.0127-0.0692i)|100> + (0.0127+0.0692i)|101> + (-0.0127+0.0692i)|110> + (0.0127-0.0692i)|111>\n  |101> -> (0.4869-0.0892i)|000> + (0.4869-0.0892i)|001> + (0.4869+0.0892i)|010> + (0.4869+0.0892i)|011> + (-0.0127-0.0692i)|100> + (-0.0127-0.0692i)|101> + (0.0127-0.0692i)|110> + (0.0127-0.0692i)|111>\n  |110> -> (-0.4869+0.0892i)|000> + (0.4869-0.0892i)|001> + (-0.4869-0.0892i)|010> + (0.4869+0.0892i)|011> + (-0.0127-0.0692i)|100> + (0.0127+0.0692i)|101> + (0.0127-0.0692i)|110> + (-0.0127+0.0692i)|111>\n  |111> -> (0.4869-0.0892i)|000> + (0.4869-0.0892i)|001> + (-0.4869-0.0892i)|010> + (-0.4869-0.0892i)|011> + (-0.0127-0.0692i)|100> + (-0.0127-0.0692i)|101> + (-0.0127+0.0692i)|110> + (-0.0127+0.0692i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ny q[1];\nry(0.6023416292820298) q[0];\ncx q[0],q[2];\nry(6.136251504521233) q[2];\ny q[1];\nh q[2];\nrx(1.381243078207626) q[1];\nx q[0];\ns q[0];\nx q[2];\nx q[1];\ny q[0];\ns q[0];\ny q[1];\nh q[1];\ncz q[1],q[2];\nry(3.089994700024885) q[0];\ncz q[1],q[0];\nx q[0];\nx q[1];\nry(1.1479538098857254) q[1];\nz q[1];\nz q[1];\nx q[1];\nry(0.2307321825133641) q[0];\nrz(0.47122629548655287) q[2];\ncx q[1],q[2];\ncx q[0],q[1];\nz q[0];\nrz(2.524388727935361) q[0];\nt q[0];\nrx(0.7925685333361148) q[0];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (0.2684-0.1571i)|000> + (0.3898+0.1606i)|001> + (-0.0350+0.2582i)|010> + (-0.4195-0.2290i)|011> + (0.0557+0.2537i)|100> + (-0.1379+0.4340i)|101> + (-0.1163+0.0286i)|110> + (0.1839-0.3260i)|111>\n  |001> -> (0.3264-0.0384i)|000> + (-0.1128-0.1835i)|001> + (0.3314+0.2344i)|010> + (0.3227-0.0770i)|011> + (-0.3613+0.3450i)|100> + (0.2051+0.0685i)|101> + (0.1011+0.4941i)|110> + (0.0819+0.1155i)|111>\n  |010> -> (-0.1364-0.0425i)|000> + (0.3259-0.1725i)|001> + (0.1076+0.1832i)|010> + (0.0705+0.4720i)|011> + (0.0789+0.2027i)|100> + (-0.4964-0.0675i)|101> + (0.3065-0.0813i)|110> + (0.3108+0.2744i)|111>\n  |011> -> (-0.0554+0.4946i)|000> + (0.0534+0.1479i)|001> + (-0.2115+0.4764i)|010> + (0.1626-0.0122i)|011> + (0.4263+0.0544i)|100> + (0.2526-0.1561i)|101> + (0.2931+0.1313i)|110> + (0.0180-0.2302i)|111>\n  |100> -> (-0.0695-0.1850i)|000> + (0.4467+0.3422i)|001> + (0.1079-0.1069i)|010> + (0.4054+0.1662i)|011> + (-0.2358+0.0828i)|100> + (0.2465-0.3009i)|101> + (-0.1748-0.1907i)|110> + (0.1255-0.3645i)|111>\n  |101> -> (-0.4261+0.1263i)|000> + (-0.0713+0.1137i)|001> + (0.2532+0.3484i)|010> + (-0.0645-0.1554i)|011> + (-0.2663+0.3291i)|100> + (0.0893+0.1668i)|101> + (0.0088-0.4723i)|110> + (-0.3230+0.1681i)|111>\n  |110> -> (-0.0394-0.2511i)|000> + (0.2972-0.2541i)|001> + (-0.2326+0.1632i)|010> + (0.0768-0.3539i)|011> + (0.0784-0.1934i)|100> + (0.4165-0.0040i)|101> + (-0.0072-0.1870i)|110> + (0.3155+0.4681i)|111>\n  |111> -> (0.1640-0.4462i)|000> + (-0.3520+0.0615i)|001> + (-0.1245+0.3817i)|010> + (0.2019+0.1228i)|011> + (0.3563+0.1968i)|100> + (-0.1292-0.1715i)|101> + (-0.4351-0.1153i)|110> + (-0.1100+0.0527i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ny q[0];\nz q[0];\nrx(3.4566600867160138) q[1];\nry(5.182820420425684) q[1];\ncz q[0],q[2];\ncz q[2],q[0];\ny q[2];\ncx q[2],q[0];\nt q[1];\nh q[0];\nt q[0];\ns q[0];\ncz q[2],q[1];\ncx q[2],q[1];\ncz q[1],q[0];\nrz(1.366671214571527) q[0];\nh q[1];\ncx q[0],q[2];\ns q[0];\ns q[1];\nh q[1];\nh q[1];\nz q[1];\nh q[0];\ncx q[2],q[1];\nh q[1];\nz q[0];\nz q[1];\ncz q[1],q[0];\ncx q[0],q[1];\ns q[1];\nx q[1];\nx q[2];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (-0.0307+0.4796i)|000> + (-0.1067-0.0876i)|001> + (0.0876-0.1067i)|010> + (0.4796+0.0307i)|011> + (-0.0411-0.1318i)|100> + (0.2890-0.3839i)|101> + (-0.3839-0.2890i)|110> + (0.1318-0.0411i)|111>\n  |001> -> (-0.0307+0.4796i)|000> + (-0.1067-0.0876i)|001> + (0.0876-0.1067i)|010> + (0.4796+0.0307i)|011> + (0.0411+0.1318i)|100> + (-0.2890+0.3839i)|101> + (0.3839+0.2890i)|110> + (-0.1318+0.0411i)|111>\n  |010> -> (0.0642+0.1223i)|000> + (0.4758+0.0671i)|001> + (-0.0671+0.4758i)|010> + (0.1223-0.0642i)|011> + (0.3608+0.3174i)|100> + (0.0135-0.1374i)|101> + (-0.1374-0.0135i)|110> + (-0.3174+0.3608i)|111>\n  |011> -> (0.0642+0.1223i)|000> + (0.4758+0.0671i)|001> + (-0.0671+0.4758i)|010> + (0.1223-0.0642i)|011> + (-0.3608-0.3174i)|100> + (-0.0135+0.1374i)|101> + (0.1374+0.0135i)|110> + (0.3174-0.3608i)|111>\n  |100> -> (0.1318-0.0411i)|000> + (0.3839+0.2890i)|001> + (0.2890-0.3839i)|010> + (0.0411+0.1318i)|011> + (-0.4796-0.0307i)|100> + (0.0876-0.1067i)|101> + (0.1067+0.0876i)|110> + (-0.0307+0.4796i)|111>\n  |101> -> (-0.1318+0.0411i)|000> + (-0.3839-0.2890i)|001> + (-0.2890+0.3839i)|010> + (-0.0411-0.1318i)|011> + (-0.4796-0.0307i)|100> + (0.0876-0.1067i)|101> + (0.1067+0.0876i)|110> + (-0.0307+0.4796i)|111>\n  |110> -> (-0.3174+0.3608i)|000> + (0.1374+0.0135i)|001> + (0.0135-0.1374i)|010> + (-0.3608-0.3174i)|011> + (-0.1223+0.0642i)|100> + (-0.0671+0.4758i)|101> + (-0.4758-0.0671i)|110> + (0.0642+0.1223i)|111>\n  |111> -> (0.3174-0.3608i)|000> + (-0.1374-0.0135i)|001> + (-0.0135+0.1374i)|010> + (0.3608+0.3174i)|011> + (-0.1223+0.0642i)|100> + (-0.0671+0.4758i)|101> + (-0.4758-0.0671i)|110> + (0.0642+0.1223i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nrz(5.576163480144678) q[0];\nx q[2];\nry(3.272651387191274) q[0];\nry(5.736650091825691) q[2];\nz q[0];\nh q[2];\ny q[2];\ncx q[2],q[0];\nrz(1.0463845822067088) q[1];\ncz q[1],q[0];\nt q[1];\nt q[1];\ny q[1];\nz q[0];\nt q[1];\nz q[1];\nz q[2];\ncx q[2],q[0];\nt q[1];\nt q[1];\nrx(5.56552043588244) q[2];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (-0.0289+0.0409i)|010> + (-0.1244-0.0880i)|011> + (0.0344+0.0244i)|110> + (0.5695-0.8051i)|111>\n  |001> -> (0.0696+0.7601i)|010> + (0.6400-0.0586i)|110> + (0.0059+0.0644i)|111>\n  |010> -> (0.4883+0.5867i)|001> + (-0.0414-0.0497i)|100> + (0.4940-0.4111i)|101>\n  |011> -> (-0.0257+0.1502i)|000> + (-0.0494-0.0085i)|001> + (-0.9720-0.1665i)|100> + (-0.0071+0.0416i)|101>\n  |100> -> (0.0244-0.0344i)|010> + (0.8051+0.5695i)|011> + (0.0409+0.0289i)|110> + (0.0880-0.1244i)|111>\n  |101> -> (-0.0586-0.6400i)|010> + (-0.0644+0.0059i)|011> + (0.7601-0.0696i)|110>\n  |110> -> (0.0497-0.0414i)|000> + (-0.4111-0.4940i)|001> + (0.5867-0.4883i)|101>\n  |111> -> (0.1665-0.9720i)|000> + (0.0416+0.0071i)|001> + (-0.1502-0.0257i)|100> + (-0.0085+0.0494i)|101>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nrx(4.358977030333853) q[1];\nt q[0];\nx q[2];\nz q[1];\nt q[1];\nrx(0.15048909201005942) q[1];\nh q[1];\nh q[0];\nz q[0];\nx q[1];\ncz q[2],q[1];\ncx q[2],q[0];\ncz q[1],q[0];\nry(3.196168710917012) q[2];\nt q[2];\ny q[1];\nry(5.274683918594714) q[1];\ncx q[0],q[1];\nx q[0];\ncz q[0],q[1];\ns q[2];\ny q[2];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (-0.0062+0.0120i)|000> + (-0.0024-0.0136i)|010> + (-0.0013+0.0179i)|011> + (-0.4710+0.1515i)|100> + (-0.2441-0.0923i)|101> + (0.2896-0.4135i)|110> + (-0.4961+0.4306i)|111>\n  |001> -> (0.0129-0.0041i)|000> + (-0.0079+0.0113i)|010> + (-0.0135+0.0118i)|011> + (0.4402+0.2260i)|100> + (-0.1074-0.2379i)|101> + (-0.4971+0.0876i)|110> + (-0.6553-0.0463i)|111>\n  |010> -> (-0.0079-0.0113i)|000> + (-0.0135-0.0118i)|001> + (-0.0129-0.0041i)|010> + (0.0876-0.4971i)|100> + (-0.0463-0.6553i)|101> + (-0.2260-0.4402i)|110> + (0.2379+0.1074i)|111>\n  |011> -> (-0.0024+0.0136i)|000> + (-0.0013-0.0179i)|001> + (0.0062+0.0120i)|010> + (-0.4135+0.2896i)|100> + (0.4306-0.4961i)|101> + (-0.1515+0.4710i)|110> + (0.0923+0.2441i)|111>\n  |100> -> (0.0463-0.6553i)|000> + (-0.0876-0.4971i)|001> + (-0.2379+0.1074i)|010> + (0.2260-0.4402i)|011> + (-0.0135+0.0118i)|100> + (-0.0079+0.0113i)|101> + (-0.0129+0.0041i)|111>\n  |101> -> (0.4961-0.4306i)|000> + (-0.2896+0.4135i)|001> + (-0.2441-0.0923i)|010> + (-0.4710+0.1515i)|011> + (-0.0179-0.0013i)|100> + (0.0136-0.0024i)|101> + (0.0120+0.0062i)|111>\n  |110> -> (-0.2441+0.0923i)|000> + (-0.4710-0.1515i)|001> + (-0.4961-0.4306i)|010> + (0.2896+0.4135i)|011> + (0.0062+0.0120i)|101> + (0.0013+0.0179i)|110> + (0.0024-0.0136i)|111>\n  |111> -> (-0.2379-0.1074i)|000> + (0.2260+0.4402i)|001> + (-0.0463-0.6553i)|010> + (0.0876-0.4971i)|011> + (0.0041-0.0129i)|101> + (-0.0118+0.0135i)|110> + (-0.0113+0.0079i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "The following 3-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nx q[1];\ny q[1];\ns q[2];\ncx q[0],q[2];\nh q[2];\ny q[0];\ns q[1];\ncz q[2],q[1];\ncz q[0],q[1];\ncx q[1],q[0];\nry(0.24307604970574218) q[2];\ns q[2];\nz q[1];\ns q[0];\nrz(4.394326520326433) q[0];\nt q[0];\nry(2.9117432417950204) q[0];\nt q[0];\nry(2.142969749756436) q[0];\ncz q[1],q[2];\ncz q[0],q[1];\nt q[2];\nrz(4.653306259731393) q[0];\nx q[0];\ns q[1];\ny q[0];\ncx q[2],q[0];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |000> -> (0.3391+0.0209i)|000> + (0.0888+0.5063i)|001> + (-0.5379-0.3773i)|100> + (-0.3254+0.2877i)|101>\n  |001> -> (0.1135-0.6472i)|000> + (-0.4335+0.0267i)|001> + (-0.2251+0.2546i)|100> + (-0.2952-0.4208i)|101>\n  |010> -> (0.6283+0.1921i)|010> + (-0.0267+0.4335i)|011> + (-0.2250-0.2546i)|110> + (-0.4538+0.2413i)|111>\n  |011> -> (0.0209+0.3391i)|010> + (0.4916-0.1502i)|011> + (0.3085-0.5801i)|110> + (0.3254+0.2877i)|111>\n  |100> -> (-0.0267+0.4335i)|000> + (-0.6472+0.1135i)|001> + (-0.2952+0.4208i)|100> + (0.2251+0.2546i)|101>\n  |101> -> (0.5063+0.0888i)|000> + (-0.0209-0.3391i)|001> + (0.3254+0.2877i)|100> + (-0.5379+0.3773i)|101>\n  |110> -> (-0.1502+0.4916i)|010> + (-0.3391-0.0209i)|011> + (-0.3254+0.2877i)|110> + (0.3085+0.5801i)|111>\n  |111> -> (-0.4335+0.0267i)|010> + (0.1921+0.6283i)|011> + (-0.4538-0.2413i)|110> + (0.2250-0.2546i)|111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "The following 4-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[2],q[3];\nh q[1];\nh q[3];\ncx q[0],q[1];\nry(2.5130239886910046) q[0];\ncx q[1],q[3];\nh q[2];\nrx(2.9813154683108953) q[0];\ny q[0];\nt q[3];\ncx q[0],q[3];\ncx q[3],q[2];\ns q[3];\ns q[1];\nrx(5.8434426255142835) q[2];\ny q[1];\ncz q[2],q[1];\nx q[3];\ncx q[2],q[1];\nry(4.382496245756494) q[2];\ns q[0];\nt q[2];\nrx(4.070412921493407) q[0];\nx q[3];\ncz q[0],q[3];\nt q[1];\nrx(2.5699231395662565) q[2];\ns q[2];\nz q[3];\nx q[0];\ncz q[2],q[0];\nrz(5.6508062204013285) q[3];\ncx q[0],q[3];\nry(0.4850419713763551) q[0];\ncz q[0],q[2];\nx q[3];\nh q[3];\ns q[2];\ny q[3];\nry(4.906137546509471) q[2];\ncz q[2],q[0];\nrz(4.6685359426428334) q[2];\ncx q[2],q[0];\ncz q[2],q[1];\nx q[1];\ncz q[3],q[0];\ncz q[3],q[2];\ncz q[3],q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |0000> -> (0.0382+0.0041i)|0000> + (-0.0124+0.0787i)|0001> + (-0.0241-0.0299i)|0010> + (0.0644-0.0469i)|0011> + (0.1571-0.1661i)|0100> + (-0.0001-0.0785i)|0101> + (0.2285-0.0064i)|0110> + (0.0555-0.0556i)|0111> + (0.0382-0.1279i)|1000> + (-0.2169-0.0640i)|1001> + (0.1174-0.0634i)|1010> + (-0.1082-0.1986i)|1011> + (0.3969+0.4333i)|1100> + (-0.1220-0.0681i)|1101> + (0.0257-0.5870i)|1110> + (0.0381+0.1344i)|1111>\n  |0001> -> (0.1077-0.1825i)|0000> + (0.0955+0.1461i)|0001> + (-0.2052+0.0529i)|0010> + (0.0358-0.1708i)|0011> + (0.1645-0.1428i)|0100> + (0.3628-0.4600i)|0101> + (0.2173+0.0153i)|0110> + (0.5818-0.0687i)|0111> + (0.0208+0.0335i)|1000> + (0.0506+0.0031i)|1001> + (-0.0090+0.0384i)|1010> + (0.0335+0.0380i)|1011> + (-0.0528-0.1077i)|1100> + (0.0950+0.0802i)|1101> + (-0.0388+0.1135i)|1110> + (-0.0105-0.1239i)|1111>\n  |0010> -> (-0.0043-0.1072i)|0000> + (-0.1077+0.1879i)|0001> + (0.0727-0.0788i)|0010> + (-0.2090+0.0568i)|0011> + (-0.0384+0.0558i)|0100> + (-0.0568+0.0030i)|0101> + (0.0666-0.0123i)|0110> + (0.0423+0.0381i)|0111> + (-0.2147-0.0813i)|1000> + (-0.4719-0.2989i)|1001> + (0.0943+0.2093i)|1010> + (0.1224+0.5451i)|1011> + (-0.1569-0.1248i)|1100> + (-0.0326+0.1665i)|1101> + (-0.0227-0.1991i)|1110> + (-0.1408+0.0947i)|1111>\n  |0011> -> (-0.2393+0.5640i)|0000> + (0.0817-0.0928i)|0001> + (-0.5680+0.2296i)|0010> + (0.1234-0.0079i)|0011> + (-0.0897-0.1086i)|0100> + (0.1874-0.1428i)|0101> + (-0.0134+0.1402i)|0110> + (-0.2335-0.0315i)|0111> + (-0.1248-0.0648i)|1000> + (-0.0610-0.0798i)|1001> + (0.0424+0.1341i)|1010> + (-0.0133+0.0995i)|1011> + (-0.0326-0.0087i)|1100> + (0.0123+0.0532i)|1101> + (-0.0169-0.0292i)|1110> + (-0.0289+0.0463i)|1111>\n  |0100> -> (-0.0741+0.1293i)|0000> + (-0.0894-0.1379i)|0001> + (-0.1438+0.0390i)|0010> + (0.0343-0.1608i)|0011> + (-0.1399+0.2750i)|0100> + (-0.1412+0.3668i)|0101> + (0.2934-0.0955i)|0110> + (0.3592-0.1595i)|0111> + (0.0001+0.0877i)|1000> + (0.1482-0.0242i)|1001> + (0.0619-0.0621i)|1010> + (-0.1219-0.0877i)|1011> + (-0.3917-0.1197i)|1100> + (0.0467-0.0301i)|1101> + (-0.1923-0.3616i)|1110> + (0.0543+0.0117i)|1111>\n  |0101> -> (-0.0033-0.1554i)|0000> + (0.0935+0.0323i)|0001> + (0.1075-0.1122i)|0010> + (0.0433+0.0889i)|0011> + (0.0635-0.0217i)|0100> + (0.1366-0.4198i)|0101> + (-0.0603-0.0296i)|0110> + (-0.3934+0.2003i)|0111> + (0.0590+0.0906i)|1000> + (0.1618-0.0706i)|1001> + (0.0223-0.1058i)|1010> + (-0.1644-0.0645i)|1011> + (-0.4259-0.1026i)|1100> + (0.1784+0.0091i)|1101> + (-0.2286-0.3737i)|1110> + (0.1197+0.1325i)|1111>\n  |0110> -> (-0.0445+0.4351i)|0000> + (0.0528-0.2358i)|0001> + (0.3391-0.2762i)|0010> + (-0.2041+0.1294i)|0011> + (-0.0555-0.1085i)|0100> + (0.1365-0.1254i)|0101> + (0.0375-0.1160i)|0110> + (0.1852+0.0079i)|0111> + (0.1021-0.0399i)|1000> + (0.3982+0.0145i)|1001> + (0.1004+0.0440i)|1010> + (0.2713+0.2918i)|1011> + (0.1355+0.0350i)|1100> + (-0.0203-0.1011i)|1101> + (-0.0710-0.1206i)|1110> + (-0.0572+0.0858i)|1111>\n  |0111> -> (-0.0251+0.4415i)|0000> + (0.0518+0.0333i)|0001> + (0.3300-0.2945i)|0010> + (-0.0131-0.0602i)|0011> + (-0.0974-0.0074i)|0100> + (0.0621-0.1433i)|0101> + (-0.0636-0.0741i)|0110> + (0.1452-0.0574i)|0111> + (-0.2422+0.0425i)|1000> + (-0.4040+0.0112i)|1001> + (-0.2013-0.1413i)|1010> + (-0.2936-0.2778i)|1011> + (-0.1471+0.0091i)|1100> + (0.0772+0.1231i)|1101> + (0.1105+0.0976i)|1110> + (0.0324-0.1417i)|1111>\n  |1000> -> (-0.0219-0.0376i)|0000> + (-0.3684-0.1755i)|0001> + (0.0110-0.0421i)|0010> + (-0.1364-0.3846i)|0011> + (-0.0963-0.1202i)|0100> + (0.0642-0.0689i)|0101> + (-0.0169+0.1531i)|0110> + (-0.0941+0.0034i)|0111> + (0.2420-0.3138i)|1000> + (-0.1296+0.2845i)|1001> + (-0.3930+0.0508i)|1010> + (0.2928-0.1095i)|1011> + (-0.1564+0.0073i)|1100> + (-0.0659+0.1238i)|1101> + (-0.1157-0.1054i)|1110> + (-0.1342+0.0409i)|1111>\n  |1001> -> (-0.1491-0.1042i)|0000> + (-0.4152-0.1439i)|0001> + (-0.0317-0.1791i)|0010> + (-0.1919-0.3954i)|0011> + (-0.0948-0.1449i)|0100> + (0.0943-0.0400i)|0101> + (-0.0354+0.1695i)|0110> + (-0.0950-0.0384i)|0111> + (-0.2072+0.3866i)|1000> + (0.0030-0.0444i)|1001> + (0.4198-0.1269i)|1010> + (-0.0335+0.0293i)|1011> + (0.0963+0.0551i)|1100> + (0.1192-0.1117i)|1101> + (0.0291+0.1071i)|1110> + (0.1632+0.0053i)|1111>\n  |1010> -> (-0.0859+0.0667i)|0000> + (-0.1266-0.0689i)|0001> + (0.1079+0.0136i)|0010> + (0.0409+0.1382i)|0011> + (0.3005+0.2594i)|0100> + (-0.0600-0.0850i)|0101> + (0.0291+0.3959i)|0110> + (0.0177-0.1025i)|0111> + (0.0284-0.1762i)|1000> + (-0.1098+0.0165i)|1001> + (0.1446-0.1045i)|1010> + (-0.0894-0.0660i)|1011> + (0.1486-0.1971i)|1100> + (0.3471-0.2709i)|1101> + (-0.2445+0.0343i)|1110> + (-0.4370-0.0539i)|1111>\n  |1011> -> (0.1295-0.0564i)|0000> + (0.1159+0.0844i)|0001> + (-0.1314-0.0516i)|0010> + (-0.0223-0.1416i)|0011> + (-0.3368-0.2261i)|0100> + (0.1713+0.1798i)|0101> + (-0.0783-0.3980i)|0110> + (-0.0060+0.2483i)|0111> + (0.0670-0.1497i)|1000> + (-0.0840-0.0708i)|1001> + (0.1533-0.0585i)|1010> + (-0.0093-0.1095i)|1011> + (-0.0343+0.0094i)|1100> + (0.3035-0.3177i)|1101> + (0.0309+0.0176i)|1110> + (-0.4393+0.0100i)|1111>\n  |1100> -> (0.1278+0.0662i)|0000> + (0.5869+0.0443i)|0001> + (-0.0435-0.1371i)|0010> + (-0.3837-0.4464i)|0011> + (0.1816+0.1303i)|0100> + (-0.0748+0.1050i)|0101> + (0.0363+0.2206i)|0110> + (-0.1272+0.0214i)|0111> + (0.0150+0.0584i)|1000> + (-0.0003-0.2230i)|1001> + (-0.0307+0.0519i)|1010> + (0.1575-0.1579i)|1011> + (0.0477-0.0812i)|1100> + (-0.0537-0.0334i)|1101> + (-0.0912+0.0237i)|1110> + (0.0143+0.0616i)|1111>\n  |1101> -> (-0.1184-0.0161i)|0000> + (-0.1117-0.0268i)|0001> + (0.0724+0.0951i)|0010> + (0.0601+0.0980i)|0011> + (-0.0267-0.0552i)|0100> + (0.0522-0.0043i)|0101> + (0.0202-0.0579i)|0110> + (0.0399+0.0339i)|0111> + (-0.0061+0.5880i)|1000> + (-0.0650-0.2139i)|1001> + (-0.4200+0.4115i)|1010> + (0.1053-0.1973i)|1011> + (0.1569-0.0574i)|1100> + (0.0298-0.2036i)|1101> + (-0.1516-0.0704i)|1110> + (-0.1651+0.1229i)|1111>\n  |1110> -> (0.1104-0.1241i)|0000> + (0.1923+0.0448i)|0001> + (0.1658-0.0097i)|0010> + (0.1043+0.1677i)|0011> + (-0.5283-0.1848i)|0100> + (0.1923+0.1301i)|0101> + (0.2429+0.5042i)|0110> + (-0.0440-0.2280i)|0111> + (0.0637+0.0412i)|1000> + (0.0167-0.0827i)|1001> + (-0.0159-0.0742i)|1010> + (-0.0702+0.0467i)|1011> + (-0.0597+0.2021i)|1100> + (-0.0113+0.0941i)|1101> + (-0.1851+0.1006i)|1110> + (-0.0745+0.0585i)|1111>\n  |1111> -> (0.0612-0.0206i)|0000> + (0.0275+0.0397i)|0001> + (0.0578+0.0287i)|0010> + (-0.0086+0.0475i)|0011> + (-0.0812-0.0479i)|0100> + (0.1242+0.0563i)|0101> + (0.0235+0.0913i)|0110> + (-0.0480-0.1276i)|0111> + (-0.0585-0.2226i)|1000> + (-0.1285+0.0279i)|1001> + (-0.1161+0.1988i)|1010> + (0.1106+0.0711i)|1011> + (-0.0308-0.1299i)|1100> + (0.1640-0.5925i)|1101> + (0.0701-0.1136i)|1110> + (0.5349-0.3030i)|1111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "The following 4-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncz q[3],q[0];\nt q[2];\nx q[2];\nx q[1];\ncx q[1],q[3];\ny q[0];\nrz(6.208256068892496) q[2];\ny q[1];\ncx q[2],q[0];\ncx q[3],q[2];\ns q[2];\nrz(0.19199770660329826) q[1];\nrz(4.713532602908841) q[3];\ns q[2];\ncx q[3],q[2];\nh q[1];\nx q[3];\nh q[0];\ncz q[1],q[0];\nrz(5.301326267231974) q[0];\ns q[0];\nz q[2];\nz q[1];\nry(1.9115838441514372) q[2];\ncx q[3],q[0];\ns q[0];\nrx(3.057876950368099) q[1];\nry(5.859570670216837) q[2];\ncx q[0],q[1];\ncz q[1],q[2];\nrx(2.2917904672326466) q[3];\ncz q[1],q[3];\ny q[2];\nx q[1];\nry(3.7277276145540488) q[1];\ncx q[3],q[2];\ncx q[1],q[3];\ny q[1];\nh q[1];\ns q[2];\ncz q[1],q[0];\nry(2.8685043881449075) q[0];\ncz q[2],q[0];\ny q[0];\ncx q[2],q[1];\nz q[2];\nrx(2.379691593995934) q[2];\ny q[2];\ns q[1];\nt q[3];\nh q[0];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |0000> -> (-0.1673+0.0328i)|0000> + (0.2571+0.2145i)|0001> + (-0.0464+0.0671i)|0010> + (-0.0581-0.2029i)|0011> + (0.0505+0.2377i)|0100> + (-0.0151-0.1700i)|0101> + (-0.2781-0.3307i)|0110> + (-0.0159-0.1804i)|0111> + (0.1409-0.2164i)|1000> + (-0.1399+0.1334i)|1001> + (0.0564-0.2280i)|1010> + (-0.2145-0.2911i)|1011> + (0.2666+0.1700i)|1100> + (-0.2318+0.1137i)|1101> + (0.1013-0.0095i)|1110> + (-0.0759+0.1652i)|1111>\n  |0001> -> (-0.3244-0.1907i)|0000> + (0.0793-0.0707i)|0001> + (0.1085+0.1568i)|0010> + (0.0224-0.0221i)|0011> + (0.0108+0.1484i)|0100> + (-0.0915-0.2142i)|0101> + (0.0821+0.2469i)|0110> + (0.3025+0.2724i)|0111> + (0.1306-0.1211i)|1000> + (-0.0872+0.2255i)|1001> + (0.2194+0.2546i)|1010> + (0.0183+0.2905i)|1011> + (0.1309-0.1689i)|1100> + (-0.3267-0.1676i)|1101> + (0.0108-0.1677i)|1110> + (-0.0582+0.0015i)|1111>\n  |0010> -> (0.2183-0.0921i)|0000> + (-0.1169+0.0890i)|0001> + (0.3949-0.0201i)|0010> + (0.2166-0.1688i)|0011> + (0.0135+0.1329i)|0100> + (-0.3578-0.0756i)|0101> + (0.0071-0.0165i)|0110> + (-0.1906+0.0472i)|0111> + (0.0942-0.3359i)|1000> + (-0.2388-0.0147i)|1001> + (-0.0347+0.0284i)|1010> + (0.1396+0.1069i)|1011> + (-0.2286-0.0968i)|1100> + (0.1734+0.0014i)|1101> + (0.2370+0.1959i)|1110> + (0.0587+0.3137i)|1111>\n  |0011> -> (-0.1304+0.1011i)|0000> + (0.2015-0.1380i)|0001> + (0.1285-0.1600i)|0010> + (0.4138-0.0877i)|0011> + (-0.3248-0.0062i)|0100> + (0.0994+0.1645i)|0101> + (-0.1784+0.1158i)|0110> + (0.0126-0.0654i)|0111> + (-0.2664+0.0940i)|1000> + (0.0439-0.2940i)|1001> + (0.1777+0.0533i)|1010> + (-0.0646+0.0591i)|1011> + (0.1849+0.0000i)|1100> + (-0.2568-0.0490i)|1101> + (0.0974+0.3338i)|1110> + (0.2367+0.1014i)|1111>\n  |0100> -> (-0.0728-0.4023i)|0000> + (0.1144+0.0152i)|0001> + (0.0443-0.1698i)|0010> + (-0.0288-0.0024i)|0011> + (-0.1146+0.1140i)|0100> + (0.1116-0.2271i)|0101> + (0.1230-0.2055i)|0110> + (0.0085-0.3746i)|0111> + (-0.1629-0.0184i)|1000> + (0.2097-0.0746i)|1001> + (-0.0543+0.3611i)|1010> + (-0.2263+0.2209i)|1011> + (-0.1964+0.0101i)|1100> + (0.0792+0.3286i)|1101> + (0.1458-0.1099i)|1110> + (-0.0424-0.0469i)|1111>\n  |0101> -> (-0.1456-0.1145i)|0000> + (0.0055+0.3637i)|0001> + (0.0747-0.0080i)|0010> + (-0.1067+0.1624i)|0011> + (-0.1600+0.2100i)|0100> + (0.1293-0.1328i)|0101> + (-0.0638+0.3925i)|0110> + (-0.1163+0.1194i)|0111> + (-0.2356+0.0316i)|1000> + (0.1771+0.0176i)|1001> + (0.2278-0.1152i)|1010> + (0.0877-0.3829i)|1011> + (-0.0414-0.2881i)|1100> + (0.2185+0.0935i)|1101> + (0.0796+0.0767i)|1110> + (-0.1898+0.0546i)|1111>\n  |0110> -> (-0.1757-0.0358i)|0000> + (0.2564+0.0681i)|0001> + (-0.1887+0.0064i)|0010> + (-0.3096-0.2360i)|0011> + (-0.2250-0.2719i)|0100> + (-0.0650+0.1984i)|0101> + (0.1879+0.0550i)|0110> + (-0.0532+0.0305i)|0111> + (0.2255+0.1294i)|1000> + (-0.2315+0.1459i)|1001> + (0.0820+0.1841i)|1010> + (-0.0945-0.0113i)|1011> + (-0.1110-0.1291i)|1100> + (0.1199+0.2086i)|1101> + (-0.2059+0.3168i)|1110> + (0.0842+0.2668i)|1111>\n  |0111> -> (0.2305+0.1145i)|0000> + (-0.1561-0.0332i)|0001> + (-0.2511-0.2635i)|0010> + (-0.2478-0.0498i)|0011> + (-0.0999+0.1053i)|0100> + (-0.1913-0.3483i)|0101> + (-0.0158+0.0049i)|0110> + (0.1473+0.1046i)|0111> + (-0.2909+0.1359i)|1000> + (0.1331+0.1754i)|1001> + (-0.0480-0.0085i)|1010> + (0.0108+0.1907i)|1011> + (0.0697+0.2176i)|1100> + (-0.1031-0.1219i)|1101> + (0.0066+0.3340i)|1110> + (-0.2168+0.2706i)|1111>\n  |1000> -> (0.0903+0.2034i)|0000> + (-0.0060+0.1638i)|0001> + (-0.2375-0.2088i)|0010> + (0.3642+0.0267i)|0011> + (-0.3216+0.1040i)|0100> + (0.0250+0.1951i)|0101> + (0.0435-0.0459i)|0110> + (-0.1207-0.1370i)|0111> + (0.1152+0.0065i)|1000> + (0.1032+0.3956i)|1001> + (-0.0289-0.0002i)|1010> + (-0.0312+0.1726i)|1011> + (0.0940-0.2350i)|1100> + (0.1056-0.1224i)|1101> + (-0.0200-0.3741i)|1110> + (-0.1070+0.2142i)|1111>\n  |1001> -> (0.0041-0.1779i)|0000> + (-0.0494-0.2325i)|0001> + (-0.3885-0.0583i)|0010> + (0.1321+0.2183i)|0011> + (0.0766-0.2249i)|0100> + (0.2841-0.0632i)|0101> + (0.0688+0.1851i)|0110> + (-0.0704+0.0852i)|0111> + (-0.0331-0.3622i)|1000> + (-0.1539-0.1031i)|1001> + (0.0941-0.1700i)|1010> + (0.0738-0.0136i)|1011> + (-0.1188+0.1423i)|1100> + (-0.1436+0.2216i)|1101> + (0.1069-0.1279i)|1110> + (-0.0338+0.3962i)|1111>\n  |1010> -> (-0.1625-0.2201i)|0000> + (0.1125-0.2344i)|0001> + (0.0043-0.0950i)|0010> + (0.1775-0.0953i)|0011> + (-0.1992+0.1350i)|0100> + (-0.1205+0.1202i)|0101> + (-0.2599+0.1036i)|0110> + (0.3311+0.1820i)|0111> + (0.2607+0.0491i)|1000> + (0.1779+0.0227i)|1001> + (-0.3262-0.2126i)|1010> + (0.1878-0.0203i)|1011> + (-0.0502+0.2027i)|1100> + (0.2444+0.2546i)|1101> + (-0.0508+0.0343i)|1110> + (-0.1914-0.0410i)|1111>\n  |1011> -> (0.1651-0.1457i)|0000> + (-0.1570-0.2801i)|0001> + (0.1894-0.0249i)|0010> + (0.0049-0.0485i)|0011> + (-0.1139+0.1118i)|0100> + (-0.2119+0.0856i)|0101> + (0.2858+0.1962i)|0110> + (-0.3326+0.0312i)|0111> + (0.1581+0.0216i)|1000> + (0.2384+0.0972i)|1001> + (0.2508+0.0314i)|1010> + (-0.2698-0.2443i)|1011> + (0.2164+0.3332i)|1100> + (-0.0918+0.1124i)|1101> + (-0.1547-0.0935i)|1110> + (-0.0154+0.0061i)|1111>\n  |1100> -> (-0.1494+0.1227i)|0000> + (-0.1565+0.2055i)|0001> + (-0.1925-0.3061i)|0010> + (-0.0730+0.2233i)|0011> + (-0.2395+0.0963i)|0100> + (-0.2533-0.1892i)|0101> + (-0.0878+0.1591i)|0110> + (-0.1017+0.0020i)|0111> + (0.2328-0.2406i)|1000> + (-0.0204-0.1692i)|1001> + (-0.2067+0.0430i)|1010> + (-0.0635-0.0512i)|1011> + (-0.1706+0.0025i)|1100> + (-0.2408+0.0328i)|1101> + (-0.1811+0.0025i)|1110> + (0.3503-0.2529i)|1111>\n  |1101> -> (0.1036-0.2185i)|0000> + (0.1392-0.1111i)|0001> + (0.0031-0.2911i)|0010> + (0.2000+0.2701i)|0011> + (0.3135+0.1912i)|0100> + (0.1429-0.1588i)|0101> + (0.0581+0.0028i)|0110> + (0.0232-0.1664i)|0111> + (0.0646+0.0843i)|1000> + (-0.2141+0.3095i)|1001> + (0.0204+0.0240i)|1010> + (0.1643-0.0966i)|1011> + (0.2204-0.0754i)|1100> + (0.1488+0.0002i)|1101> + (-0.2940+0.2815i)|1110> + (0.2523-0.0636i)|1111>\n  |1110> -> (-0.2370-0.0328i)|0000> + (-0.1195+0.3278i)|0001> + (0.1311+0.1172i)|0010> + (0.0368-0.0257i)|0011> + (0.1728+0.0146i)|0100> + (0.2206+0.1139i)|0101> + (0.0346+0.3172i)|0110> + (-0.2214-0.2134i)|0111> + (0.0798+0.1233i)|1000> + (0.0753+0.2247i)|1001> + (-0.1519-0.2288i)|1010> + (-0.0100+0.3953i)|1011> + (-0.1026+0.3510i)|1100> + (-0.1335+0.0034i)|1101> + (0.0326+0.1936i)|1110> + (0.0159+0.0084i)|1111>\n  |1111> -> (-0.0661+0.2898i)|0000> + (-0.2727+0.0735i)|0001> + (0.0689-0.0540i)|0010> + (0.1731+0.0666i)|0011> + (0.2523+0.0684i)|0100> + (0.1844+0.0141i)|0101> + (-0.2283-0.1191i)|0110> + (0.0718+0.3403i)|0111> + (0.1223+0.2114i)|1000> + (0.0909+0.1377i)|1001> + (0.0560+0.4193i)|1010> + (-0.1497-0.1403i)|1011> + (-0.1716+0.0866i)|1100> + (-0.0309+0.3234i)|1101> + (0.0643+0.0176i)|1110> + (0.1019+0.1867i)|1111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "The following 4-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nrz(4.98675651542124) q[1];\ncz q[3],q[0];\ncz q[3],q[2];\nrz(2.5907257657475737) q[2];\nx q[1];\ns q[1];\nt q[1];\nt q[1];\ncz q[2],q[1];\ncx q[1],q[2];\nt q[3];\ny q[3];\ncz q[1],q[0];\ncx q[1],q[0];\ncx q[0],q[3];\nrx(4.69553845940479) q[1];\ncz q[1],q[2];\nh q[1];\ncx q[0],q[3];\nt q[0];\nh q[1];\nh q[1];\ny q[2];\nrx(4.7996101619797065) q[3];\nry(2.8433055314440168) q[0];\ny q[2];\ncz q[0],q[1];\ns q[0];\nx q[2];\ns q[1];\ncz q[0],q[1];\ny q[2];\nt q[3];\nz q[3];\nry(0.48415689123877803) q[3];\ny q[1];\nrz(1.089133865252038) q[1];\ncx q[0],q[2];\nrz(4.198225315561197) q[1];\ny q[1];\ncz q[1],q[3];\ny q[0];\nrx(1.0992218314728714) q[0];\nt q[0];\nrx(1.0955904870926036) q[3];\ny q[3];\ncz q[3],q[0];\ncx q[1],q[0];\nry(2.1439258631110696) q[2];\ny q[0];\nz q[0];\nz q[2];\ncx q[1],q[0];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |0000> -> (-0.0214-0.0838i)|0000> + (-0.0420+0.0814i)|0001> + (0.0949+0.1862i)|0010> + (0.0559-0.2141i)|0011> + (0.0935+0.1737i)|0100> + (0.0309-0.0947i)|0101> + (-0.3126-0.3600i)|0110> + (-0.0226+0.2397i)|0111> + (0.0227+0.2231i)|1000> + (-0.1389+0.1926i)|1001> + (-0.0255+0.1160i)|1010> + (-0.1018+0.0739i)|1011> + (-0.1732-0.4815i)|1100> + (0.1155-0.2311i)|1101> + (-0.0075-0.2709i)|1110> + (0.0964-0.0971i)|1111>\n  |0001> -> (-0.1197-0.0520i)|0000> + (-0.0687-0.1646i)|0001> + (0.3098+0.0592i)|0010> + (0.2493+0.3516i)|0011> + (-0.0355-0.0032i)|0100> + (-0.0670-0.1006i)|0101> + (0.0853-0.0113i)|0110> + (0.2112+0.2015i)|0111> + (0.2871+0.1794i)|1000> + (-0.1131-0.4485i)|1001> + (0.1148+0.1378i)|1010> + (0.0174-0.2444i)|1011> + (0.0897+0.0217i)|1100> + (-0.1332-0.2836i)|1101> + (0.0415+0.0258i)|1110> + (-0.0201-0.1647i)|1111>\n  |0010> -> (0.0659+0.0636i)|0000> + (-0.0036+0.0864i)|0001> + (-0.1928-0.1086i)|0010> + (-0.0443-0.2042i)|0011> + (-0.0819-0.0568i)|0100> + (-0.0397-0.1933i)|0101> + (0.2260+0.0829i)|0110> + (0.2106+0.4277i)|0111> + (-0.1446-0.1884i)|1000> + (-0.0423+0.2202i)|1001> + (-0.0455-0.1172i)|1010> + (-0.0542+0.1057i)|1011> + (0.1882+0.1770i)|1100> + (-0.0277-0.5110i)|1101> + (0.0694+0.1179i)|1110> + (0.0618-0.2639i)|1111>\n  |0011> -> (-0.0185-0.1774i)|0000> + (-0.0842+0.0997i)|0001> + (0.1515+0.4035i)|0010> + (0.1361-0.2846i)|0011> + (-0.0353-0.1155i)|0100> + (-0.0132+0.0330i)|0101> + (0.1529+0.2487i)|0110> + (0.0108-0.0853i)|0111> + (-0.0205+0.4621i)|1000> + (-0.2543+0.2235i)|1001> + (-0.0790+0.2319i)|1010> + (-0.1625+0.0759i)|1011> + (0.0462+0.3099i)|1100> + (-0.0466+0.0797i)|1101> + (-0.0225+0.1644i)|1110> + (-0.0355+0.0336i)|1111>\n  |0100> -> (-0.1067+0.1429i)|0000> + (0.1295-0.0161i)|0001> + (-0.1624+0.3992i)|0010> + (0.2931-0.1167i)|0011> + (-0.0525+0.1088i)|0100> + (0.0321-0.0153i)|0101> + (-0.0563+0.2865i)|0110> + (0.0658-0.0554i)|0111> + (0.3286-0.3256i)|1000> + (0.3384+0.0083i)|1001> + (-0.2154+0.1168i)|1010> + (-0.1708-0.0545i)|1011> + (0.1763-0.2590i)|1100> + (0.0883-0.0269i)|1101> + (-0.1281+0.1055i)|1110> + (-0.0489+0.0006i)|1111>\n  |0101> -> (0.0053+0.0914i)|0000> + (-0.0612+0.0611i)|0001> + (0.0680+0.2106i)|0010> + (-0.1059+0.1801i)|0011> + (-0.0216-0.0972i)|0100> + (0.1020-0.1689i)|0101> + (-0.1098-0.2142i)|0110> + (0.1354-0.4572i)|0111> + (0.0216-0.2365i)|1000> + (-0.1805+0.1331i)|1001> + (-0.0461+0.1170i)|1010> + (0.1115-0.0409i)|1011> + (0.0181+0.2577i)|1100> + (0.3263-0.3942i)|1101> + (0.0290-0.1337i)|1110> + (-0.2244+0.1520i)|1111>\n  |0110> -> (-0.0174+0.1294i)|0000> + (-0.1396+0.1110i)|0001> + (0.0276+0.3142i)|0010> + (-0.2702+0.3358i)|0011> + (0.0066+0.0350i)|0100> + (-0.0784+0.0919i)|0101> + (0.0342+0.0789i)|0110> + (-0.1362+0.2582i)|0111> + (0.0942-0.3252i)|1000> + (-0.4006+0.2312i)|1001> + (-0.1012+0.1480i)|1010> + (0.2398-0.0500i)|1011> + (-0.0036-0.0922i)|1100> + (-0.2364+0.2056i)|1101> + (-0.0135+0.0470i)|1110> + (0.1530-0.0643i)|1111>\n  |0111> -> (0.0748-0.0435i)|0000> + (-0.0897-0.0182i)|0001> + (0.1532-0.1421i)|0010> + (-0.2212+0.0047i)|0011> + (-0.1416+0.1374i)|0100> + (0.0995+0.0039i)|0101> + (-0.2610+0.3990i)|0110> + (0.2367-0.0437i)|0111> + (-0.2084+0.0828i)|1000> + (-0.2232-0.0811i)|1001> + (0.1186-0.0072i)|1010> + (0.0989+0.0777i)|1011> + (0.4159-0.2981i)|1100> + (0.2538+0.0481i)|1101> + (-0.2586+0.0811i)|1110> + (-0.1197-0.0662i)|1111>\n  |1000> -> (-0.2169+0.0571i)|0000> + (0.2118+0.1074i)|0001> + (0.0143+0.1179i)|0010> + (0.0716-0.1034i)|0011> + (0.4488-0.2458i)|0100> + (-0.2462-0.0783i)|0101> + (-0.0966-0.2532i)|0110> + (-0.0589+0.1235i)|0111> + (-0.0860+0.0094i)|1000> + (-0.0746-0.0530i)|1001> + (0.1122-0.1763i)|1010> + (0.2128-0.0606i)|1011> + (0.1852-0.0681i)|1100> + (0.0894+0.0439i)|1101> + (-0.1515+0.4521i)|1110> + (-0.2179+0.1022i)|1111>\n  |1001> -> (0.1327-0.3115i)|0000> + (0.4256-0.1812i)|0001> + (-0.1538-0.0921i)|0010> + (-0.0644-0.2364i)|0011> + (0.0076-0.0920i)|0100> + (0.2595-0.1756i)|0101> + (-0.0477-0.0106i)|0110> + (-0.0734-0.1488i)|0111> + (0.0684-0.1112i)|1000> + (-0.1726+0.0448i)|1001> + (0.1063+0.2970i)|1010> + (0.1764-0.3933i)|1011> + (0.0081-0.0347i)|1100> + (-0.1090+0.0522i)|1101> + (0.0530+0.0677i)|1110> + (0.0664-0.2843i)|1111>\n  |1010> -> (0.1637-0.1720i)|0000> + (0.2241+0.0076i)|0001> + (-0.0817-0.0956i)|0010> + (0.0162-0.1177i)|0011> + (-0.1457+0.2133i)|0100> + (-0.5005+0.1066i)|0101> + (0.1044+0.0884i)|0110> + (0.0289+0.2695i)|0111> + (0.0722-0.0563i)|1000> + (-0.0850-0.0157i)|1001> + (0.0044+0.2212i)|1010> + (0.1534-0.1419i)|1011> + (-0.0677+0.0730i)|1100> + (0.1970-0.0121i)|1101> + (-0.0433-0.2368i)|1110> + (-0.2616+0.3986i)|1111>\n  |1011> -> (0.4597-0.0514i)|0000> + (-0.2602-0.2165i)|0001> + (-0.0020-0.2450i)|0010> + (-0.1283+0.1253i)|0011> + (0.2990-0.0937i)|0100> + (-0.0859-0.0337i)|0101> + (-0.0331-0.1626i)|0110> + (-0.0224+0.0434i)|0111> + (0.1783+0.0066i)|1000> + (0.0869+0.0974i)|1001> + (-0.2708+0.3354i)|1010> + (-0.3143+0.0272i)|1011> + (0.1194-0.0187i)|1100> + (0.0309+0.0177i)|1101> + (-0.1366+0.2580i)|1110> + (-0.0790+0.0340i)|1111>\n  |1100> -> (-0.3726-0.2741i)|0000> + (0.0443+0.3356i)|0001> + (0.1647-0.1814i)|0010> + (-0.1792+0.0050i)|0011> + (-0.2832-0.1340i)|0100> + (0.0403+0.0830i)|0101> + (0.0860-0.1419i)|0110> + (-0.0459+0.0167i)|0111> + (-0.1265-0.1258i)|1000> + (0.0022-0.1305i)|1001> + (-0.4264+0.0627i)|1010> + (-0.2493-0.1933i)|1011> + (-0.1004-0.0673i)|1100> + (-0.0106-0.0340i)|1101> + (-0.2754+0.0969i)|1110> + (-0.0811-0.0286i)|1111>\n  |1101> -> (0.2370-0.0154i)|0000> + (0.1595+0.1576i)|0001> + (-0.0048+0.1257i)|0010> + (-0.0917+0.0754i)|0011> + (-0.2518+0.0579i)|0100> + (-0.4400-0.2612i)|0101> + (-0.0168-0.1358i)|0110> + (0.1616-0.2176i)|0111> + (0.0913+0.0077i)|1000> + (-0.0518-0.0692i)|1001> + (0.1469-0.1655i)|1010> + (-0.2090+0.0001i)|1011> + (-0.0993+0.0077i)|1100> + (0.1529+0.1247i)|1101> + (-0.1288+0.2034i)|1110> + (0.4626-0.1154i)|1111>\n  |1110> -> (-0.3358-0.0426i)|0000> + (-0.2905-0.3600i)|0001> + (0.0466-0.1731i)|0010> + (0.2098-0.1264i)|0011> + (-0.0906+0.0178i)|0100> + (-0.2398-0.2017i)|0101> + (-0.0028-0.0488i)|0110> + (0.1231-0.1112i)|0111> + (-0.1257-0.0354i)|1000> + (0.0903+0.1538i)|1001> + (-0.2567+0.1833i)|1010> + (0.4265+0.0624i)|1011> + (-0.0356+0.0016i)|1100> + (0.0799+0.0906i)|1101> + (-0.0507+0.0695i)|1110> + (0.2916-0.0137i)|1111>\n  |1111> -> (-0.1141-0.1931i)|0000> + (-0.0455+0.2331i)|0001> + (0.1095-0.0459i)|0010> + (-0.1190-0.0407i)|0011> + (0.3590+0.3647i)|0100> + (0.0081-0.2582i)|0101> + (-0.2173+0.1620i)|0110> + (0.1349+0.0229i)|0111> + (-0.0325-0.0801i)|1000> + (0.0306-0.0863i)|1001> + (-0.2002-0.0599i)|1010> + (-0.1164-0.1882i)|1011> + (0.1161+0.1595i)|1100> + (-0.0178+0.0980i)|1101> + (0.4763+0.0223i)|1110> + (0.1578+0.1818i)|1111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "The following 4-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nx q[0];\ncz q[3],q[0];\nry(2.4258308371489203) q[3];\ncz q[2],q[3];\nt q[0];\nh q[0];\nh q[1];\ns q[2];\ny q[1];\nt q[3];\ny q[3];\nrz(4.97320825750158) q[2];\ncx q[3],q[1];\nt q[3];\nry(3.5048648242575777) q[2];\ncz q[1],q[3];\nh q[2];\nrx(1.9322388056630297) q[3];\ncz q[2],q[1];\ncz q[2],q[0];\ncz q[2],q[0];\nry(2.8673857507137934) q[0];\ny q[1];\ncz q[1],q[3];\ncx q[1],q[2];\nh q[2];\ny q[3];\ncx q[3],q[2];\ncz q[2],q[1];\ny q[0];\nz q[0];\ncz q[1],q[2];\nrz(3.6803672216376744) q[0];\nt q[0];\nh q[0];\ncx q[3],q[0];\nh q[2];\nx q[1];\ncz q[1],q[3];\ncx q[0],q[3];\ncz q[2],q[0];\nt q[2];\nx q[1];\ns q[3];\nz q[1];\nh q[0];\nx q[0];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |0000> -> (0.2510-0.0845i)|0000> + (0.0764+0.0933i)|0001> + (0.0974-0.0940i)|0010> + (0.2686+0.1269i)|0011> + (-0.1471+0.2581i)|0100> + (-0.1337-0.0211i)|0101> + (0.0090-0.1203i)|0110> + (0.2540-0.0748i)|0111> + (-0.4315+0.1697i)|1000> + (0.1419+0.1565i)|1001> + (-0.0891-0.0224i)|1010> + (0.0231+0.2004i)|1011> + (-0.0137+0.2012i)|1100> + (0.0880-0.0266i)|1101> + (0.1344-0.1630i)|1110> + (-0.4389-0.1495i)|1111>\n  |0001> -> (0.2905+0.1697i)|0000> + (-0.0255+0.1512i)|0001> + (0.1714+0.0147i)|0010> + (0.1028+0.3632i)|0011> + (-0.3700+0.0747i)|0100> + (-0.0915-0.1457i)|0101> + (0.1227-0.0918i)|0110> + (0.2838+0.1807i)|0111> + (0.3239+0.1681i)|1000> + (0.0194-0.1651i)|1001> + (0.0328+0.0645i)|1010> + (0.1069-0.1174i)|1011> + (0.1264-0.0960i)|1100> + (-0.0613-0.0384i)|1101> + (-0.1662+0.0046i)|1110> + (0.1384+0.3376i)|1111>\n  |0010> -> (0.1143-0.0385i)|0000> + (0.1678+0.2049i)|0001> + (-0.2137+0.2064i)|0010> + (-0.1224-0.0578i)|0011> + (-0.0670+0.1176i)|0100> + (-0.2934-0.0464i)|0101> + (-0.0198+0.2641i)|0110> + (-0.1157+0.0341i)|0111> + (-0.1966+0.0773i)|1000> + (0.3114+0.3436i)|1001> + (0.1956+0.0493i)|1010> + (-0.0105-0.0913i)|1011> + (-0.0063+0.0917i)|1100> + (0.1931-0.0583i)|1101> + (-0.2950+0.3577i)|1110> + (0.2000+0.0681i)|1111>\n  |0011> -> (0.1324+0.0773i)|0000> + (-0.0560+0.3317i)|0001> + (-0.3761-0.0323i)|0010> + (-0.0468-0.1655i)|0011> + (-0.1686+0.0340i)|0100> + (-0.2007-0.3197i)|0101> + (-0.2694+0.2016i)|0110> + (-0.1293-0.0823i)|0111> + (0.1476+0.0766i)|1000> + (0.0427-0.3624i)|1001> + (-0.0720-0.1415i)|1010> + (-0.0487+0.0535i)|1011> + (0.0576-0.0437i)|1100> + (-0.1345-0.0843i)|1101> + (0.3648-0.0101i)|1110> + (-0.0631-0.1538i)|1111>\n  |0100> -> (-0.1183+0.0657i)|0000> + (-0.2268-0.1919i)|0001> + (0.2643-0.0169i)|0010> + (0.0498+0.1099i)|0011> + (-0.0398+0.1139i)|0100> + (-0.2647+0.0068i)|0101> + (-0.2087+0.2114i)|0110> + (-0.1237-0.0549i)|0111> + (0.0803+0.0447i)|1000> + (0.0294-0.1995i)|1001> + (-0.4607+0.0527i)|1010> + (0.0967+0.1878i)|1011> + (-0.1719+0.1228i)|1100> + (0.3855+0.2576i)|1101> + (-0.0652+0.1909i)|1110> + (0.0918-0.0030i)|1111>\n  |0101> -> (-0.1618-0.0584i)|0000> + (-0.0057-0.3774i)|0001> + (0.2369+0.2389i)|0010> + (-0.0636+0.1395i)|0011> + (-0.1423+0.0571i)|0100> + (-0.2276-0.2478i)|0101> + (-0.3768-0.0232i)|0110> + (-0.0508-0.1643i)|0111> + (-0.0151-0.0707i)|1000> + (-0.1335+0.0858i)|1001> + (0.2696+0.2459i)|1010> + (0.0614-0.1545i)|1011> + (0.1618+0.0384i)|1100> + (-0.0467-0.3619i)|1101> + (0.1469-0.0601i)|1110> + (-0.0493-0.0529i)|1111>\n  |0110> -> (-0.2597+0.1443i)|0000> + (-0.1033-0.0874i)|0001> + (-0.1204+0.0077i)|0010> + (-0.1093-0.2412i)|0011> + (-0.0873+0.2500i)|0100> + (-0.1206+0.0031i)|0101> + (0.0951-0.0963i)|0110> + (0.2716+0.1205i)|0111> + (0.1763+0.0980i)|1000> + (0.0134-0.0909i)|1001> + (0.2099-0.0240i)|1010> + (-0.2122-0.4123i)|1011> + (-0.3773+0.2695i)|1100> + (0.1757+0.1174i)|1101> + (0.0297-0.0870i)|1110> + (-0.2016+0.0066i)|1111>\n  |0111> -> (-0.3550-0.1282i)|0000> + (-0.0026-0.1720i)|0001> + (-0.1079-0.1088i)|0010> + (0.1397-0.3061i)|0011> + (-0.3123+0.1253i)|0100> + (-0.1037-0.1129i)|0101> + (0.1717+0.0106i)|0110> + (0.1115+0.3606i)|0111> + (-0.0331-0.1553i)|1000> + (-0.0608+0.0391i)|1001> + (-0.1228-0.1121i)|1010> + (-0.1347+0.3392i)|1011> + (0.3551+0.0843i)|1100> + (-0.0213-0.1649i)|1101> + (-0.0669+0.0274i)|1110> + (0.1082+0.1162i)|1111>\n  |1000> -> (0.1143-0.0385i)|0000> + (-0.1678-0.2049i)|0001> + (-0.2137+0.2064i)|0010> + (0.1224+0.0578i)|0011> + (-0.0670+0.1176i)|0100> + (0.2934+0.0464i)|0101> + (-0.0198+0.2641i)|0110> + (0.1157-0.0341i)|0111> + (-0.1966+0.0773i)|1000> + (-0.3114-0.3436i)|1001> + (0.1956+0.0493i)|1010> + (0.0105+0.0913i)|1011> + (-0.0063+0.0917i)|1100> + (-0.1931+0.0583i)|1101> + (-0.2950+0.3577i)|1110> + (-0.2000-0.0681i)|1111>\n  |1001> -> (-0.1324-0.0773i)|0000> + (-0.0560+0.3317i)|0001> + (0.3761+0.0323i)|0010> + (-0.0468-0.1655i)|0011> + (0.1686-0.0340i)|0100> + (-0.2007-0.3197i)|0101> + (0.2694-0.2016i)|0110> + (-0.1293-0.0823i)|0111> + (-0.1476-0.0766i)|1000> + (0.0427-0.3624i)|1001> + (0.0720+0.1415i)|1010> + (-0.0487+0.0535i)|1011> + (-0.0576+0.0437i)|1100> + (-0.1345-0.0843i)|1101> + (-0.3648+0.0101i)|1110> + (-0.0631-0.1538i)|1111>\n  |1010> -> (-0.2510+0.0845i)|0000> + (0.0764+0.0933i)|0001> + (-0.0974+0.0940i)|0010> + (0.2686+0.1269i)|0011> + (0.1471-0.2581i)|0100> + (-0.1337-0.0211i)|0101> + (-0.0090+0.1203i)|0110> + (0.2540-0.0748i)|0111> + (0.4315-0.1697i)|1000> + (0.1419+0.1565i)|1001> + (0.0891+0.0224i)|1010> + (0.0231+0.2004i)|1011> + (0.0137-0.2012i)|1100> + (0.0880-0.0266i)|1101> + (-0.1344+0.1630i)|1110> + (-0.4389-0.1495i)|1111>\n  |1011> -> (0.2905+0.1697i)|0000> + (0.0255-0.1512i)|0001> + (0.1714+0.0147i)|0010> + (-0.1028-0.3632i)|0011> + (-0.3700+0.0747i)|0100> + (0.0915+0.1457i)|0101> + (0.1227-0.0918i)|0110> + (-0.2838-0.1807i)|0111> + (0.3239+0.1681i)|1000> + (-0.0194+0.1651i)|1001> + (0.0328+0.0645i)|1010> + (-0.1069+0.1174i)|1011> + (0.1264-0.0960i)|1100> + (0.0613+0.0384i)|1101> + (-0.1662+0.0046i)|1110> + (-0.1384-0.3376i)|1111>\n  |1100> -> (0.2597-0.1443i)|0000> + (-0.1033-0.0874i)|0001> + (0.1204-0.0077i)|0010> + (-0.1093-0.2412i)|0011> + (0.0873-0.2500i)|0100> + (-0.1206+0.0031i)|0101> + (-0.0951+0.0963i)|0110> + (0.2716+0.1205i)|0111> + (-0.1763-0.0980i)|1000> + (0.0134-0.0909i)|1001> + (-0.2099+0.0240i)|1010> + (-0.2122-0.4123i)|1011> + (0.3773-0.2695i)|1100> + (0.1757+0.1174i)|1101> + (-0.0297+0.0870i)|1110> + (-0.2016+0.0066i)|1111>\n  |1101> -> (-0.3550-0.1282i)|0000> + (0.0026+0.1720i)|0001> + (-0.1079-0.1088i)|0010> + (-0.1397+0.3061i)|0011> + (-0.3123+0.1253i)|0100> + (0.1037+0.1129i)|0101> + (0.1717+0.0106i)|0110> + (-0.1115-0.3606i)|0111> + (-0.0331-0.1553i)|1000> + (0.0608-0.0391i)|1001> + (-0.1228-0.1121i)|1010> + (0.1347-0.3392i)|1011> + (0.3551+0.0843i)|1100> + (0.0213+0.1649i)|1101> + (-0.0669+0.0274i)|1110> + (-0.1082-0.1162i)|1111>\n  |1110> -> (-0.1183+0.0657i)|0000> + (0.2268+0.1919i)|0001> + (0.2643-0.0169i)|0010> + (-0.0498-0.1099i)|0011> + (-0.0398+0.1139i)|0100> + (0.2647-0.0068i)|0101> + (-0.2087+0.2114i)|0110> + (0.1237+0.0549i)|0111> + (0.0803+0.0447i)|1000> + (-0.0294+0.1995i)|1001> + (-0.4607+0.0527i)|1010> + (-0.0967-0.1878i)|1011> + (-0.1719+0.1228i)|1100> + (-0.3855-0.2576i)|1101> + (-0.0652+0.1909i)|1110> + (-0.0918+0.0030i)|1111>\n  |1111> -> (0.1618+0.0584i)|0000> + (-0.0057-0.3774i)|0001> + (-0.2369-0.2389i)|0010> + (-0.0636+0.1395i)|0011> + (0.1423-0.0571i)|0100> + (-0.2276-0.2478i)|0101> + (0.3768+0.0232i)|0110> + (-0.0508-0.1643i)|0111> + (0.0151+0.0707i)|1000> + (-0.1335+0.0858i)|1001> + (-0.2696-0.2459i)|1010> + (0.0614-0.1545i)|1011> + (-0.1618-0.0384i)|1100> + (-0.0467-0.3619i)|1101> + (-0.1469+0.0601i)|1110> + (-0.0493-0.0529i)|1111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "The following 4-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nrz(2.739822209913614) q[0];\ny q[2];\nz q[0];\ncz q[3],q[1];\ncz q[3],q[1];\ncz q[2],q[1];\ns q[3];\nrz(0.39301171691285414) q[1];\nh q[0];\nx q[3];\ncx q[3],q[0];\nt q[3];\nz q[1];\ncx q[3],q[1];\nrx(1.586927554328436) q[2];\ns q[1];\nz q[1];\nh q[2];\nry(1.234869319072365) q[1];\ncx q[1],q[3];\ny q[1];\ny q[0];\nz q[3];\nx q[3];\nh q[1];\ncz q[0],q[3];\nh q[2];\nt q[0];\nt q[0];\ncz q[0],q[2];\nh q[2];\nry(5.520680537892614) q[1];\nz q[3];\nh q[3];\ncz q[2],q[1];\ny q[3];\ncx q[1],q[2];\nrx(3.6820866227845843) q[0];\nrz(6.141028870304362) q[2];\nz q[0];\nry(2.8506968082199733) q[2];\ncx q[0],q[3];\nz q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |0000> -> (0.3351+0.0742i)|0000> + (0.3286-0.0209i)|0001> + (0.0863-0.0877i)|0010> + (-0.0632+0.0654i)|0011> + (-0.0260+0.3282i)|0100> + (-0.0736-0.3366i)|0101> + (0.0665-0.0630i)|0110> + (0.0878-0.0850i)|0111> + (0.1926+0.1054i)|1000> + (0.1706+0.0532i)|1001> + (-0.0438+0.2882i)|1010> + (-0.0426-0.2885i)|1011> + (0.0506+0.1705i)|1100> + (-0.1050-0.1944i)|1101> + (-0.2881-0.0432i)|1110> + (-0.2880+0.0392i)|1111>\n  |0001> -> (-0.2802+0.1453i)|0000> + (0.2635-0.2391i)|0001> + (0.0894+0.0199i)|0010> + (0.1173+0.0356i)|0011> + (-0.0186-0.3566i)|0100> + (-0.1004-0.2992i)|0101> + (-0.1079-0.0565i)|0110> + (0.0783+0.0486i)|0111> + (-0.1113+0.1328i)|1000> + (0.1201-0.1888i)|1001> + (-0.1058-0.2589i)|1010> + (-0.1893-0.2366i)|1011> + (0.0475-0.2201i)|1100> + (0.0126-0.1720i)|1101> + (0.2998-0.0380i)|1110> + (-0.2574+0.1087i)|1111>\n  |0010> -> (-0.1115+0.0470i)|0000> + (-0.0847+0.0370i)|0001> + (-0.2808-0.2026i)|0010> + (0.3131+0.1017i)|0011> + (-0.0841+0.0324i)|0100> + (0.1155-0.0455i)|0101> + (0.1451-0.2956i)|0110> + (0.0652-0.3352i)|0111> + (-0.1460+0.2500i)|1000> + (-0.0753+0.2811i)|1001> + (0.1383+0.1747i)|1010> + (-0.1370-0.1116i)|1011> + (-0.2479-0.1544i)|1100> + (0.2841+0.0702i)|1101> + (-0.0167+0.1790i)|1110> + (0.0206+0.2168i)|1111>\n  |0011> -> (-0.0760-0.0536i)|0000> + (0.0933+0.0764i)|0001> + (0.3148-0.0216i)|0010> + (0.3361-0.1254i)|0011> + (0.0794+0.0949i)|0100> + (0.0527+0.0739i)|0101> + (-0.1139+0.3353i)|0110> + (0.0272-0.3144i)|0111> + (-0.0032-0.2790i)|1000> + (0.0796+0.2904i)|1001> + (-0.1529+0.0773i)|1010> + (-0.1850+0.1316i)|1011> + (0.2922+0.0843i)|1100> + (0.2800-0.0065i)|1101> + (0.1250-0.1834i)|1110> + (-0.0803+0.1549i)|1111>\n  |0100> -> (-0.3365+0.1194i)|0000> + (0.3148-0.0219i)|0001> + (-0.0935-0.0780i)|0010> + (-0.0749-0.0537i)|0011> + (-0.0269+0.3144i)|0100> + (-0.1200+0.3350i)|0101> + (-0.0526-0.0749i)|0110> + (0.0778+0.0948i)|0111> + (-0.1852+0.1282i)|1000> + (0.1540-0.0775i)|1001> + (0.0797+0.2915i)|1010> + (-0.0019+0.2794i)|1011> + (-0.0800+0.1537i)|1100> + (-0.1284+0.1833i)|1101> + (0.2797-0.0015i)|1110> + (-0.2911-0.0842i)|1111>\n  |0101> -> (0.2933-0.1497i)|0000> + (0.3391-0.0609i)|0001> + (-0.0328+0.0855i)|0010> + (0.0449-0.1136i)|0011> + (-0.1968-0.2811i)|0100> + (0.1066+0.3115i)|0101> + (0.0479-0.1133i)|0110> + (0.0362-0.0835i)|0111> + (0.1768-0.0185i)|1000> + (0.2198+0.0225i)|1001> + (-0.1503-0.2496i)|1010> + (0.0741+0.2811i)|1011> + (-0.1711-0.1376i)|1100> + (0.1144+0.1372i)|1101> + (-0.2495+0.1508i)|1110> + (-0.2828+0.0711i)|1111>\n  |0110> -> (0.0572+0.1097i)|0000> + (-0.0481-0.0769i)|0001> + (0.3534+0.0231i)|0010> + (0.3009+0.0953i)|0011> + (0.0204+0.0907i)|0100> + (0.0348+0.1155i)|0101> + (0.1405-0.2825i)|0110> + (-0.2445+0.2625i)|0111> + (-0.0340+0.3022i)|1000> + (0.1133-0.2562i)|1001> + (-0.2173+0.0453i)|1010> + (-0.1738+0.0148i)|1011> + (0.2565+0.1098i)|1100> + (0.2378+0.1847i)|1101> + (-0.1299+0.1116i)|1110> + (0.1924-0.1205i)|1111>\n  |0111> -> (0.0622-0.0653i)|0000> + (0.0862-0.0893i)|0001> + (-0.3286+0.0209i)|0010> + (0.3346+0.0682i)|0011> + (-0.0862+0.0850i)|0100> + (0.0666-0.0641i)|0101> + (0.0796+0.3370i)|0110> + (-0.0260+0.3282i)|0111> + (-0.0477-0.2881i)|1000> + (0.0439-0.2893i)|1001> + (0.1717+0.0531i)|1010> + (-0.1923-0.1020i)|1011> + (-0.2869+0.0391i)|1100> + (0.2885+0.0381i)|1101> + (-0.1084-0.1947i)|1110> + (-0.0507-0.1693i)|1111>\n  |1000> -> (0.0150+0.0909i)|0000> + (0.0109+0.1213i)|0001> + (-0.2381-0.2071i)|0010> + (0.3224+0.1536i)|0011> + (0.0120-0.1220i)|0100> + (-0.0158+0.0902i)|0101> + (0.3217-0.1520i)|0110> + (0.2414-0.2033i)|0111> + (0.1989-0.1962i)|1000> + (0.1498-0.2625i)|1001> + (-0.1637-0.0541i)|1010> + (0.2216+0.0403i)|1011> + (0.1463+0.2654i)|1100> + (-0.1988-0.1967i)|1101> + (0.2204-0.0388i)|1110> + (0.1653-0.0521i)|1111>\n  |1001> -> (-0.1121+0.0486i)|0000> + (0.0837-0.0373i)|0001> + (-0.2828-0.1967i)|0010> + (-0.3132-0.1015i)|0011> + (-0.0846+0.0334i)|0100> + (-0.1140+0.0462i)|0101> + (0.1449-0.2956i)|0110> + (-0.0596+0.3380i)|0111> + (0.1464-0.2511i)|1000> + (-0.0703+0.2828i)|1001> + (-0.1395-0.1714i)|1010> + (-0.1382-0.1119i)|1011> + (0.2503+0.1497i)|1100> + (0.2831+0.0697i)|1101> + (0.0161-0.1779i)|1110> + (0.0237+0.2183i)|1111>\n  |1010> -> (0.1453+0.2802i)|0000> + (0.2335+0.2662i)|0001> + (0.0204-0.0884i)|0010> + (-0.0371+0.1180i)|0011> + (-0.3585+0.0127i)|0100> + (0.2992-0.1004i)|0101> + (-0.0570+0.1063i)|0110> + (-0.0497+0.0786i)|0111> + (-0.1334-0.1124i)|1000> + (-0.1857-0.1217i)|1001> + (0.2612-0.1010i)|1010> + (-0.2377+0.1896i)|1011> + (0.2212+0.0508i)|1100> + (-0.1708-0.0130i)|1101> + (0.0375+0.2988i)|1110> + (0.1037+0.2590i)|1111>\n  |1011> -> (0.1884+0.2848i)|0000> + (-0.2471-0.2176i)|0001> + (0.1241-0.0022i)|0010> + (0.0901-0.0022i)|0011> + (-0.2504+0.2137i)|0100> + (-0.1820+0.2945i)|0101> + (0.0924+0.0018i)|0110> + (-0.1211-0.0008i)|0111> + (-0.0639-0.2082i)|1000> + (0.0839+0.1590i)|1001> + (0.2356-0.1735i)|1010> + (0.1700-0.2375i)|1011> + (0.0839-0.1555i)|1100> + (0.0610-0.2143i)|1101> + (0.1770+0.2309i)|1110> + (-0.2305-0.1752i)|1111>\n  |1100> -> (0.0910-0.0015i)|0000> + (-0.1230+0.0010i)|0001> + (-0.2471-0.2176i)|0010> + (-0.1845-0.2894i)|0011> + (-0.1222-0.0020i)|0100> + (-0.0916-0.0024i)|0101> + (-0.1860+0.2900i)|0110> + (0.2504-0.2137i)|0111> + (-0.1739+0.2342i)|1000> + (0.2348-0.1728i)|1001> + (-0.0830-0.1582i)|1010> + (-0.0617-0.2107i)|1011> + (0.2314+0.1759i)|1100> + (0.1732+0.2343i)|1101> + (-0.0632+0.2117i)|1110> + (0.0848-0.1563i)|1111>\n  |1101> -> (-0.0578-0.1081i)|0000> + (-0.0491-0.0772i)|0001> + (-0.3554-0.0172i)|0010> + (0.3008+0.0954i)|0011> + (-0.0210-0.0898i)|0100> + (0.0363+0.1162i)|0101> + (-0.1406+0.2825i)|0110> + (-0.2390+0.2653i)|0111> + (-0.0335+0.3012i)|1000> + (-0.1083+0.2579i)|1001> + (-0.2185+0.0486i)|1010> + (0.1726-0.0152i)|1011> + (0.2589+0.1051i)|1100> + (-0.2389-0.1851i)|1101> + (-0.1305+0.1127i)|1110> + (-0.1892+0.1221i)|1111>\n  |1110> -> (0.1495+0.2933i)|0000> + (-0.0553-0.3418i)|0001> + (-0.0860-0.0338i)|0010> + (-0.1121-0.0456i)|0011> + (0.2831-0.1909i)|0100> + (0.3116-0.1064i)|0101> + (0.1138+0.0495i)|0110> + (-0.0824-0.0365i)|0111> + (-0.0179-0.1758i)|1000> + (-0.0257+0.2213i)|1001> + (-0.2520+0.1455i)|1010> + (-0.2800+0.0736i)|1011> + (-0.1387+0.1678i)|1100> + (-0.1384+0.1147i)|1101> + (0.1512+0.2505i)|1110> + (-0.0661-0.2845i)|1111>\n  |1111> -> (0.3263+0.1490i)|0000> + (0.2379+0.2073i)|0001> + (0.0120+0.1200i)|0010> + (-0.0158-0.0916i)|0011> + (0.2416-0.2031i)|0100> + (-0.3176+0.1565i)|0101> + (-0.0150+0.0895i)|0110> + (-0.0109+0.1232i)|0111> + (-0.2238-0.0378i)|1000> + (-0.1628-0.0535i)|1001> + (-0.1491+0.2616i)|1010> + (0.1950-0.1995i)|1011> + (-0.1663+0.0528i)|1100> + (0.2181-0.0413i)|1101> + (0.2026+0.1934i)|1110> + (0.1470+0.2662i)|1111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "The following 5-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\nrz(5.655195634596385) q[2];\ncz q[4],q[2];\nz q[0];\ncz q[4],q[1];\nx q[1];\ncz q[4],q[1];\ncx q[4],q[0];\nh q[0];\ncx q[1],q[2];\nx q[1];\ncx q[2],q[3];\nx q[2];\ncz q[1],q[4];\ncx q[0],q[3];\nx q[2];\ncx q[2],q[0];\ncx q[4],q[3];\ncz q[1],q[3];\nx q[1];\ncz q[3],q[4];\ncz q[2],q[3];\ny q[1];\ncx q[4],q[1];\ny q[1];\nrx(2.3620671057185727) q[0];\ncz q[2],q[4];\nry(6.014813233512013) q[2];\nx q[3];\nry(1.251801085655153) q[2];\nrx(5.227142850173022) q[3];\nrz(0.5892156730760137) q[1];\ncz q[4],q[2];\ncx q[1],q[0];\nx q[2];\ncx q[3],q[4];\nry(4.382101640568701) q[1];\ncz q[2],q[4];\nx q[3];\nt q[0];\ny q[2];\nz q[1];\nh q[4];\ncx q[2],q[0];\ns q[4];\ns q[4];\ncx q[4],q[1];\nrx(3.128898118538559) q[1];\ny q[4];\nry(5.904337709273202) q[4];\ncz q[3],q[1];\nz q[0];\nz q[1];\nrz(4.3730986066586315) q[4];\ncx q[3],q[1];\nz q[2];\ncx q[0],q[2];\nt q[2];\ncx q[3],q[2];\nz q[0];\ncx q[2],q[1];\nrx(0.22827291980121459) q[1];\ny q[4];\ncz q[1],q[0];\ncz q[4],q[2];\ncx q[3],q[1];\nx q[0];\nrx(3.164635891029958) q[0];\nrz(3.2707456305640883) q[1];\nt q[0];\nz q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00000> -> (-0.1046-0.1521i)|00000> + (-0.0195+0.0969i)|00001> + (-0.1059-0.2804i)|00010> + (0.0638-0.1473i)|00011> + (-0.0100-0.0200i)|00100> + (-0.0126+0.0397i)|00101> + (-0.0066-0.0121i)|00110> + (0.0076-0.0245i)|00111> + (0.1644-0.0428i)|01000> + (-0.2759-0.1563i)|01001> + (-0.2070+0.0457i)|01010> + (-0.3303-0.2180i)|01011> + (-0.0523+0.0173i)|01100> + (0.0261+0.0137i)|01101> + (0.0436-0.0067i)|01110> + (0.0193+0.0137i)|01111> + (-0.3904+0.0637i)|10000> + (0.1701+0.1264i)|10001> + (-0.3158+0.0315i)|10010> + (-0.1332-0.1057i)|10011> + (0.0232-0.0047i)|10100> + (-0.0372-0.0238i)|10101> + (0.0294-0.0018i)|10110> + (0.0406+0.0371i)|10111> + (-0.0024+0.1607i)|11000> + (0.2121-0.2122i)|11001> + (0.0208-0.0964i)|11010> + (0.1563-0.0974i)|11011> + (-0.0028+0.0255i)|11100> + (0.0109-0.0084i)|11101> + (0.0049-0.0415i)|11110> + (0.0173-0.0141i)|11111>\n  |00001> -> (-0.0641-0.0933i)|00000> + (-0.0120+0.0595i)|00001> + (-0.0650-0.1720i)|00010> + (0.0392-0.0904i)|00011> + (0.0575+0.1152i)|00100> + (0.0727-0.2291i)|00101> + (0.0381+0.0696i)|00110> + (-0.0437+0.1414i)|00111> + (-0.1009+0.0262i)|01000> + (0.1693+0.0959i)|01001> + (0.1270-0.0280i)|01010> + (0.2026+0.1337i)|01011> + (-0.3014+0.0995i)|01100> + (0.1507+0.0788i)|01101> + (0.2513-0.0388i)|01110> + (0.1111+0.0788i)|01111> + (-0.2395+0.0391i)|10000> + (0.1044+0.0775i)|10001> + (-0.1937+0.0193i)|10010> + (-0.0817-0.0648i)|10011> + (-0.1336+0.0272i)|10100> + (0.2144+0.1371i)|10101> + (-0.1696+0.0102i)|10110> + (-0.2342-0.2140i)|10111> + (0.0015-0.0986i)|11000> + (-0.1301+0.1301i)|11001> + (-0.0128+0.0591i)|11010> + (-0.0959+0.0597i)|11011> + (-0.0164+0.1467i)|11100> + (0.0625-0.0484i)|11101> + (0.0280-0.2389i)|11110> + (0.0999-0.0814i)|11111>\n  |00010> -> (0.0177-0.0236i)|00000> + (0.0546-0.0069i)|00001> + (-0.0181+0.0152i)|00010> + (0.0441+0.0031i)|00011> + (-0.2081+0.2396i)|00100> + (-0.1694+0.0145i)|00101> + (0.2844-0.2750i)|00110> + (-0.2118-0.0068i)|00111> + (-0.0367-0.0200i)|01000> + (-0.0066-0.0214i)|01001> + (-0.0221-0.0129i)|01010> + (0.0033+0.0133i)|01011> + (-0.0919-0.0359i)|01100> + (-0.0713-0.1697i)|01101> + (-0.1274-0.0980i)|01110> + (0.0433+0.2968i)|01111> + (0.0064+0.0122i)|10000> + (-0.0080+0.0244i)|10001> + (-0.0095-0.0202i)|10010> + (-0.0136+0.0394i)|10011> + (0.1677+0.2484i)|10100> + (-0.0281+0.1581i)|10101> + (-0.0595-0.1747i)|10110> + (-0.0450+0.0880i)|10111> + (-0.0307+0.0317i)|11000> + (-0.0236+0.0008i)|11001> + (-0.0451+0.0316i)|11010> + (0.0290+0.0055i)|11011> + (0.1524-0.1474i)|11100> + (0.3956+0.0128i)|11101> + (0.1357-0.1022i)|11110> + (-0.3147-0.0395i)|11111>\n  |00011> -> (0.1022-0.1358i)|00000> + (0.3148-0.0395i)|00001> + (-0.1044+0.0877i)|00010> + (0.2539+0.0181i)|00011> + (0.1277-0.1470i)|00100> + (0.1039-0.0089i)|00101> + (-0.1744+0.1687i)|00110> + (0.1299+0.0042i)|00111> + (0.2112+0.1151i)|01000> + (0.0383+0.1230i)|01001> + (0.1275+0.0745i)|01010> + (-0.0189-0.0768i)|01011> + (-0.0564-0.0220i)|01100> + (-0.0438-0.1041i)|01101> + (-0.0781-0.0601i)|01110> + (0.0266+0.1821i)|01111> + (0.0370+0.0701i)|10000> + (-0.0459+0.1407i)|10001> + (-0.0545-0.1166i)|10010> + (-0.0786+0.2271i)|10011> + (-0.1029-0.1524i)|10100> + (0.0173-0.0970i)|10101> + (0.0365+0.1072i)|10110> + (0.0276-0.0540i)|10111> + (0.1768-0.1828i)|11000> + (0.1362-0.0044i)|11001> + (0.2599-0.1823i)|11010> + (-0.1670-0.0320i)|11011> + (0.0935-0.0904i)|11100> + (0.2427+0.0078i)|11101> + (0.0833-0.0627i)|11110> + (-0.1930-0.0242i)|11111>\n  |00100> -> (-0.0577-0.0187i)|00000> + (-0.0500-0.1016i)|00001> + (-0.0808-0.0564i)|00010> + (0.0350+0.1805i)|00011> + (-0.2162-0.1051i)|00100> + (-0.0439-0.1210i)|00101> + (-0.1320-0.0670i)|00110> + (0.0235+0.0757i)|00111> + (0.1194-0.1536i)|01000> + (0.1032-0.0146i)|01001> + (-0.1661+0.1771i)|01010> + (0.1301-0.0022i)|01011> + (-0.0955+0.1407i)|01100> + (-0.3126+0.0549i)|01101> + (0.0994-0.0932i)|01110> + (-0.2543-0.0042i)|01111> + (-0.0889+0.0948i)|10000> + (-0.2426+0.0040i)|10001> + (-0.0798+0.0672i)|10010> + (0.1942+0.0137i)|10011> + (0.1667-0.1923i)|10100> + (0.1358-0.0118i)|10101> + (0.2505-0.1946i)|10110> + (-0.1683-0.0237i)|10111> + (0.1100+0.1476i)|11000> + (-0.0127+0.0978i)|11001> + (-0.0427-0.1046i)|11010> + (-0.0243+0.0554i)|11011> + (0.0410+0.0677i)|11100> + (-0.0374+0.1428i)|11101> + (-0.0599-0.1141i)|11110> + (-0.0680+0.2308i)|11111>\n  |00101> -> (0.0941+0.0304i)|00000> + (0.0815+0.1656i)|00001> + (0.1317+0.0919i)|00010> + (-0.0570-0.2942i)|00011> + (-0.0375-0.0182i)|00100> + (-0.0076-0.0210i)|00101> + (-0.0229-0.0116i)|00110> + (0.0041+0.0131i)|00111> + (0.1946-0.2504i)|01000> + (0.1682-0.0237i)|01001> + (-0.2707+0.2888i)|01010> + (0.2120-0.0036i)|01011> + (0.0166-0.0244i)|01100> + (0.0542-0.0095i)|01101> + (-0.0172+0.0162i)|01110> + (0.0441+0.0007i)|01111> + (0.1450-0.1546i)|10000> + (0.3955-0.0066i)|10001> + (0.1301-0.1095i)|10010> + (-0.3166-0.0223i)|10011> + (0.0289-0.0334i)|10100> + (0.0236-0.0020i)|10101> + (0.0435-0.0338i)|10110> + (-0.0292-0.0041i)|10111> + (0.1793+0.2405i)|11000> + (-0.0208+0.1594i)|11001> + (-0.0696-0.1705i)|11010> + (-0.0396+0.0903i)|11011> + (-0.0071-0.0117i)|11100> + (0.0065-0.0248i)|11101> + (0.0104+0.0198i)|11110> + (0.0118-0.0400i)|11111>\n  |00110> -> (-0.0142+0.3169i)|00000> + (0.1272-0.1127i)|00001> + (0.0546-0.2486i)|00010> + (0.1137-0.0752i)|00011> + (0.0120-0.1036i)|00100> + (-0.1507+0.1233i)|00101> + (-0.0190+0.1286i)|00110> + (-0.1970+0.1417i)|00111> + (0.1282-0.0130i)|01000> + (-0.1887-0.1491i)|01001> + (0.0785-0.0100i)|01010> + (0.1154+0.0922i)|01011> + (0.1100-0.0255i)|01100> + (-0.0509-0.0328i)|01101> + (0.1840+0.0000i)|01110> + (0.0708+0.0686i)|01111> + (-0.1309-0.0691i)|10000> + (0.0223+0.0761i)|10001> + (0.2134+0.1106i)|10010> + (0.0408+0.1221i)|10011> + (-0.0916-0.0362i)|10100> + (0.0757+0.1676i)|10101> + (0.0505+0.0336i)|10110> + (0.0206+0.1113i)|10111> + (0.0228-0.1343i)|11000> + (-0.2051+0.1503i)|11001> + (0.0508-0.1623i)|11010> + (0.2835-0.1428i)|11011> + (-0.0487+0.2379i)|11100> + (0.1096-0.0700i)|11101> + (-0.0519+0.1875i)|11110> + (-0.0899+0.0528i)|11111>\n  |00111> -> (0.0025-0.0550i)|00000> + (-0.0221+0.0196i)|00001> + (-0.0095+0.0431i)|00010> + (-0.0197+0.0131i)|00011> + (0.0195-0.1689i)|00100> + (-0.2456+0.2010i)|00101> + (-0.0309+0.2097i)|00110> + (-0.3211+0.2310i)|00111> + (0.0222-0.0023i)|01000> + (-0.0328-0.0259i)|01001> + (0.0136-0.0017i)|01010> + (0.0200+0.0160i)|01011> + (-0.1794+0.0416i)|01100> + (0.0829+0.0534i)|01101> + (-0.3000-0.0000i)|01110> + (-0.1154-0.1119i)|01111> + (0.0227+0.0120i)|10000> + (-0.0039-0.0132i)|10001> + (-0.0370-0.0192i)|10010> + (-0.0071-0.0212i)|10011> + (-0.1493-0.0590i)|10100> + (0.1234+0.2731i)|10101> + (0.0823+0.0548i)|10110> + (0.0336+0.1815i)|10111> + (0.0040-0.0233i)|11000> + (-0.0356+0.0261i)|11001> + (0.0088-0.0282i)|11010> + (0.0492-0.0248i)|11011> + (0.0794-0.3878i)|11100> + (-0.1787+0.1141i)|11101> + (0.0846-0.3057i)|11110> + (0.1465-0.0860i)|11111>\n  |01000> -> (-0.0212+0.0145i)|00000> + (0.0135+0.0027i)|00001> + (-0.0390+0.0147i)|00010> + (-0.0205-0.0089i)|00011> + (0.1437-0.0717i)|00100> + (-0.2857-0.0907i)|00101> + (0.0867-0.0475i)|00110> + (0.1763+0.0545i)|00111> + (-0.0060-0.0229i)|01000> + (-0.0218+0.0384i)|01001> + (0.0064+0.0288i)|01010> + (-0.0303+0.0460i)|01011> + (-0.1241-0.3759i)|01100> + (-0.0983+0.1879i)|01101> + (0.0484+0.3134i)|01110> + (-0.0983+0.1386i)|01111> + (0.0089+0.0543i)|10000> + (0.0176-0.0237i)|10001> + (0.0044+0.0439i)|10010> + (-0.0147+0.0185i)|10011> + (0.0339+0.1666i)|10100> + (0.1710-0.2674i)|10101> + (0.0128+0.2115i)|10110> + (-0.2669+0.2920i)|10111> + (0.0224+0.0003i)|11000> + (-0.0295-0.0295i)|11001> + (-0.0134-0.0029i)|11010> + (-0.0136-0.0217i)|11011> + (-0.1830-0.0204i)|11100> + (0.0604+0.0780i)|11101> + (0.2979+0.0349i)|11110> + (0.1016+0.1245i)|11111>\n  |01001> -> (-0.1220+0.0838i)|00000> + (0.0777+0.0156i)|00001> + (-0.2248+0.0849i)|00010> + (-0.1181-0.0512i)|00011> + (-0.0881+0.0440i)|00100> + (0.1752+0.0556i)|00101> + (-0.0532+0.0291i)|00110> + (-0.1082-0.0335i)|00111> + (0.0343+0.1318i)|01000> + (0.1254-0.2213i)|01001> + (-0.0367-0.1660i)|01010> + (0.1748-0.2649i)|01011> + (-0.0761-0.2306i)|01100> + (-0.0603+0.1153i)|01101> + (0.0297+0.1923i)|01110> + (-0.0603+0.0850i)|01111> + (0.0511+0.3131i)|10000> + (0.1014-0.1364i)|10001> + (0.0253+0.2533i)|10010> + (-0.0847+0.1068i)|10011> + (-0.0208-0.1022i)|10100> + (-0.1049+0.1640i)|10101> + (-0.0078-0.1298i)|10110> + (0.1637-0.1791i)|10111> + (-0.1289-0.0020i)|11000> + (0.1701+0.1701i)|11001> + (0.0773+0.0167i)|11010> + (0.0781+0.1253i)|11011> + (-0.1122-0.0125i)|11100> + (0.0370+0.0478i)|11101> + (0.1828+0.0214i)|11110> + (0.0623+0.0764i)|11111>\n  |01010> -> (0.1693+0.1274i)|00000> + (0.0493+0.3925i)|00001> + (-0.1094-0.1302i)|00010> + (-0.0226+0.3166i)|00011> + (0.0333+0.0290i)|00100> + (0.0020+0.0236i)|00101> + (-0.0383-0.0396i)|00110> + (-0.0009+0.0295i)|00111> + (0.1435-0.2634i)|01000> + (0.1534-0.0478i)|01001> + (0.0929-0.1590i)|01010> + (-0.0958+0.0235i)|01011> + (-0.0050+0.0128i)|01100> + (-0.0236+0.0099i)|01101> + (-0.0136+0.0177i)|01110> + (0.0413-0.0060i)|01111> + (-0.0875+0.0461i)|10000> + (-0.1755-0.0573i)|10001> + (0.1455-0.0680i)|10010> + (-0.2833-0.0980i)|10011> + (0.0346-0.0233i)|10100> + (0.0220+0.0039i)|10101> + (-0.0243+0.0083i)|10110> + (0.0123+0.0063i)|10111> + (-0.2280-0.2205i)|11000> + (-0.0054-0.1698i)|11001> + (-0.2273-0.3241i)|11010> + (-0.0399+0.2083i)|11011> + (-0.0205-0.0212i)|11100> + (0.0018-0.0550i)|11101> + (-0.0142-0.0189i)|11110> + (-0.0055+0.0438i)|11111>\n  |01011> -> (0.1039+0.0782i)|00000> + (0.0302+0.2408i)|00001> + (-0.0671-0.0799i)|00010> + (-0.0139+0.1942i)|00011> + (-0.1922-0.1669i)|00100> + (-0.0117-0.1358i)|00101> + (0.2205+0.2280i)|00110> + (0.0054-0.1699i)|00111> + (-0.0881+0.1616i)|01000> + (-0.0941+0.0293i)|01001> + (-0.0570+0.0975i)|01010> + (0.0588-0.0144i)|01011> + (-0.0288+0.0737i)|01100> + (-0.1361+0.0572i)|01101> + (-0.0786+0.1021i)|01110> + (0.2380-0.0347i)|01111> + (-0.0537+0.0283i)|10000> + (-0.1076-0.0351i)|10001> + (0.0892-0.0417i)|10010> + (-0.1738-0.0601i)|10011> + (-0.1992+0.1345i)|10100> + (-0.1268-0.0226i)|10101> + (0.1401-0.0477i)|10110> + (-0.0706-0.0361i)|10111> + (0.1398+0.1352i)|11000> + (0.0033+0.1042i)|11001> + (0.1394+0.1988i)|11010> + (0.0245-0.1278i)|11011> + (-0.1182-0.1222i)|11100> + (0.0102-0.3172i)|11101> + (-0.0819-0.1088i)|11110> + (-0.0317+0.2523i)|11111>\n  |01100> -> (0.0244-0.0754i)|00000> + (0.1328-0.0653i)|00001> + (0.0737-0.1056i)|00010> + (-0.2359+0.0457i)|00011> + (-0.0804+0.1654i)|00100> + (-0.0926+0.0336i)|00101> + (-0.0513+0.1010i)|00110> + (0.0579-0.0179i)|00111> + (0.2008+0.1560i)|01000> + (0.0190+0.1349i)|01001> + (-0.2316-0.2171i)|01010> + (0.0029+0.1700i)|01011> + (0.1076+0.0730i)|01100> + (0.0420+0.2391i)|01101> + (-0.0713-0.0760i)|01110> + (-0.0032+0.1945i)|01111> + (-0.1240-0.1163i)|10000> + (-0.0053-0.3172i)|10001> + (-0.0878-0.1043i)|10010> + (-0.0179+0.2539i)|10011> + (-0.1471-0.1275i)|10100> + (-0.0090-0.1039i)|10101> + (-0.1489-0.1916i)|10110> + (-0.0182+0.1287i)|10111> + (-0.1929+0.1438i)|11000> + (-0.1278-0.0167i)|11001> + (0.1367-0.0558i)|11010> + (-0.0724-0.0318i)|11011> + (0.0518-0.0313i)|11100> + (0.1093+0.0286i)|11101> + (-0.0873+0.0458i)|11110> + (0.1765+0.0520i)|11111>\n  |01101> -> (-0.0042+0.0131i)|00000> + (-0.0230+0.0113i)|00001> + (-0.0128+0.0183i)|00010> + (0.0409-0.0079i)|00011> + (-0.1310+0.2696i)|00100> + (-0.1509+0.0548i)|00101> + (-0.0835+0.1646i)|00110> + (0.0945-0.0292i)|00111> + (0.0348+0.0271i)|01000> + (0.0033+0.0234i)|01001> + (-0.0402-0.0377i)|01010> + (0.0005+0.0295i)|01011> + (-0.1754-0.1191i)|01100> + (-0.0684-0.3898i)|01101> + (0.1162+0.1239i)|01110> + (0.0053-0.3171i)|01111> + (0.0215+0.0202i)|10000> + (0.0009+0.0550i)|10001> + (0.0152+0.0181i)|10010> + (0.0031-0.0441i)|10011> + (-0.2398-0.2079i)|10100> + (-0.0147-0.1694i)|10101> + (-0.2427-0.3124i)|10110> + (-0.0296+0.2098i)|10111> + (-0.0335+0.0249i)|11000> + (-0.0222-0.0029i)|11001> + (0.0237-0.0097i)|11010> + (-0.0126-0.0055i)|11011> + (-0.0844+0.0511i)|11100> + (-0.1781-0.0467i)|11101> + (0.1423-0.0747i)|11110> + (-0.2878-0.0848i)|11111>\n  |01110> -> (0.2424+0.0109i)|00000> + (-0.0862-0.0973i)|00001> + (-0.1902-0.0418i)|00010> + (-0.0575-0.0870i)|00011> + (0.1354+0.0156i)|00100> + (-0.1612-0.1970i)|00101> + (-0.1681-0.0248i)|00110> + (-0.1853-0.2575i)|00111> + (-0.0100-0.0981i)|01000> + (-0.1141+0.1444i)|01001> + (-0.0076-0.0600i)|01010> + (0.0705-0.0882i)|01011> + (0.0334+0.1438i)|01100> + (0.0429-0.0665i)|01101> + (-0.0000+0.2406i)|01110> + (-0.0897+0.0925i)|01111> + (-0.0528+0.1001i)|10000> + (0.0582-0.0170i)|10001> + (0.0846-0.1632i)|10010> + (0.0934-0.0312i)|10011> + (0.0473-0.1197i)|10100> + (-0.2190+0.0989i)|10101> + (-0.0439+0.0660i)|10110> + (-0.1455+0.0270i)|10111> + (-0.1027-0.0175i)|11000> + (0.1150+0.1569i)|11001> + (-0.1241-0.0389i)|11010> + (-0.1092-0.2169i)|11011> + (-0.3109-0.0637i)|11100> + (0.0915+0.1433i)|11101> + (-0.2451-0.0678i)|11110> + (-0.0690-0.1175i)|11111>\n  |01111> -> (-0.3952-0.0178i)|00000> + (0.1406+0.1586i)|00001> + (0.3100+0.0681i)|00010> + (0.0938+0.1418i)|00011> + (0.0235+0.0027i)|00100> + (-0.0280-0.0342i)|00101> + (-0.0292-0.0043i)|00110> + (-0.0321-0.0447i)|00111> + (-0.0163-0.1599i)|01000> + (-0.1860+0.2354i)|01001> + (-0.0125-0.0978i)|01010> + (0.1149-0.1438i)|01011> + (-0.0058-0.0250i)|01100> + (-0.0074+0.0115i)|01101> + (0.0000-0.0417i)|01110> + (0.0156-0.0161i)|01111> + (0.0861-0.1633i)|10000> + (-0.0949+0.0278i)|10001> + (-0.1379+0.2661i)|10010> + (-0.1523+0.0509i)|10011> + (0.0082-0.0208i)|10100> + (-0.0380+0.0172i)|10101> + (-0.0076+0.0115i)|10110> + (-0.0253+0.0047i)|10111> + (-0.1675-0.0285i)|11000> + (0.1874+0.2558i)|11001> + (-0.2023-0.0634i)|11010> + (-0.1780-0.3535i)|11011> + (0.0540+0.0111i)|11100> + (-0.0159-0.0249i)|11101> + (0.0425+0.0118i)|11110> + (0.0120+0.0204i)|11111>\n  |10000> -> (0.2386+0.1814i)|00000> + (-0.0192-0.1594i)|00001> + (-0.1160-0.1435i)|00010> + (0.0089-0.0985i)|00011> + (-0.0097-0.0098i)|00100> + (0.0003+0.0257i)|00101> + (0.0163+0.0153i)|00110> + (0.0008+0.0417i)|00111> + (-0.1028+0.1855i)|01000> + (0.3787-0.1150i)|01001> + (-0.0878+0.1454i)|01010> + (-0.3090+0.0713i)|01011> + (-0.0189+0.0399i)|01100> + (0.0224-0.0076i)|01101> + (-0.0314+0.0452i)|01110> + (-0.0290+0.0057i)|01111> + (0.2779-0.1533i)|10000> + (-0.1626-0.0497i)|10001> + (-0.3576+0.1691i)|10010> + (-0.2006-0.0683i)|10011> + (0.0252-0.0152i)|10100> + (-0.0536-0.0124i)|10101> + (-0.0218+0.0093i)|10110> + (-0.0407-0.0171i)|10111> + (-0.0719-0.0676i)|11000> + (0.0085+0.1839i)|11001> + (-0.0932-0.1309i)|11010> + (0.0543-0.2950i)|11011> + (0.0275+0.0314i)|11100> + (0.0018-0.0223i)|11101> + (0.0168+0.0193i)|11110> + (-0.0008+0.0137i)|11111>\n  |10001> -> (-0.1464-0.1113i)|00000> + (0.0118+0.0978i)|00001> + (0.0712+0.0880i)|00010> + (-0.0055+0.0604i)|00011> + (-0.0558-0.0563i)|00100> + (0.0017+0.1480i)|00101> + (0.0941+0.0879i)|00110> + (0.0045+0.2403i)|00111> + (-0.0630+0.1138i)|01000> + (0.2323-0.0705i)|01001> + (-0.0539+0.0892i)|01010> + (-0.1896+0.0437i)|01011> + (0.1087-0.2299i)|01100> + (-0.1290+0.0439i)|01101> + (0.1812-0.2606i)|01110> + (0.1669-0.0326i)|01111> + (-0.1705+0.0940i)|10000> + (0.0997+0.0305i)|10001> + (0.2194-0.1038i)|10010> + (0.1231+0.0419i)|10011> + (0.1455-0.0878i)|10100> + (-0.3091-0.0713i)|10101> + (-0.1254+0.0534i)|10110> + (-0.2346-0.0987i)|10111> + (-0.0441-0.0414i)|11000> + (0.0052+0.1128i)|11001> + (-0.0572-0.0803i)|11010> + (0.0333-0.1810i)|11011> + (-0.1587-0.1808i)|11100> + (-0.0104+0.1285i)|11101> + (-0.0968-0.1115i)|11110> + (0.0044-0.0790i)|11111>\n  |10010> -> (0.0197-0.0130i)|00000> + (0.0431+0.0095i)|00001> + (0.0276-0.0103i)|00010> + (-0.0504-0.0221i)|00011> + (0.3446-0.1943i)|00100> + (0.2050+0.0538i)|00101> + (0.2890-0.1313i)|00110> + (-0.1583-0.0622i)|00111> + (-0.0061-0.0249i)|01000> + (0.0069-0.0118i)|01001> + (0.0087+0.0408i)|01010> + (0.0124-0.0186i)|01011> + (0.0577+0.1500i)|01100> + (-0.1260+0.2722i)|01101> + (-0.0082-0.0983i)|01110> + (-0.1167+0.1424i)|01111> + (0.0037+0.0220i)|10000> + (-0.0247+0.0336i)|10001> + (0.0016+0.0137i)|10010> + (0.0156-0.0204i)|10011> + (-0.0502-0.1776i)|10100> + (0.0470-0.0870i)|10101> + (-0.0029-0.2997i)|10110> + (-0.1142+0.1129i)|10111> + (-0.0551-0.0004i)|11000> + (-0.0210-0.0207i)|11001> + (0.0433+0.0087i)|11010> + (-0.0128-0.0199i)|11011> + (-0.1697-0.0071i)|11100> + (-0.2111-0.2367i)|11101> + (0.2092+0.0348i)|11110> + (-0.2350-0.3185i)|11111>\n  |10011> -> (-0.1138+0.0751i)|00000> + (-0.2485-0.0549i)|00001> + (-0.1593+0.0593i)|00010> + (0.2905+0.1275i)|00011> + (0.2114-0.1192i)|00100> + (0.1257+0.0330i)|00101> + (0.1773-0.0805i)|00110> + (-0.0971-0.0381i)|00111> + (-0.0351-0.1434i)|01000> + (0.0400-0.0683i)|01001> + (0.0502+0.2353i)|01010> + (0.0717-0.1071i)|01011> + (-0.0354-0.0920i)|01100> + (0.0773-0.1670i)|01101> + (0.0050+0.0603i)|01110> + (0.0716-0.0874i)|01111> + (-0.0213-0.1270i)|10000> + (0.1424-0.1936i)|10001> + (-0.0094-0.0787i)|10010> + (-0.0898+0.1177i)|10011> + (-0.0308-0.1090i)|10100> + (0.0288-0.0534i)|10101> + (-0.0018-0.1838i)|10110> + (-0.0700+0.0692i)|10111> + (-0.3174-0.0026i)|11000> + (-0.1211-0.1194i)|11001> + (0.2493+0.0502i)|11010> + (-0.0737-0.1146i)|11011> + (0.1041+0.0043i)|11100> + (0.1295+0.1452i)|11101> + (-0.1283-0.0214i)|11110> + (0.1442+0.1954i)|11111>\n  |10100> -> (-0.0985+0.0006i)|00000> + (-0.1288-0.1312i)|00001> + (0.0581+0.0174i)|00010> + (-0.0553-0.0988i)|00011> + (0.1467+0.0197i)|00100> + (0.0490+0.0623i)|00101> + (-0.2376-0.0362i)|00110> + (0.0747+0.1049i)|00111> + (-0.0362-0.2401i)|01000> + (0.0756-0.1058i)|01001> + (-0.0111-0.1942i)|01010> + (-0.0706+0.0767i)|01011> + (-0.0289-0.1331i)|01100> + (0.1408-0.2118i)|01101> + (0.0012-0.1700i)|01110> + (-0.2226+0.2263i)|01111> + (-0.0417+0.0956i)|10000> + (-0.1823+0.0684i)|10001> + (0.0656-0.1123i)|10010> + (-0.2337+0.0652i)|10011> + (-0.1153+0.2955i)|10100> + (-0.1546+0.0707i)|10101> + (0.1369-0.2146i)|10110> + (-0.1336+0.0274i)|10111> + (0.1124+0.0111i)|11000> + (0.0391+0.0462i)|11001> + (0.1728+0.0634i)|11010> + (-0.0400-0.0901i)|11011> + (-0.1264-0.0250i)|11100> + (-0.1309-0.2019i)|11101> + (-0.0765-0.0200i)|11110> + (0.0766+0.1263i)|11111>\n  |10101> -> (-0.1606+0.0009i)|00000> + (-0.2099-0.2139i)|00001> + (0.0947+0.0283i)|00010> + (-0.0901-0.1611i)|00011> + (-0.0255-0.0034i)|00100> + (-0.0085-0.0108i)|00101> + (0.0412+0.0063i)|00110> + (-0.0130-0.0182i)|00111> + (0.0590+0.3914i)|01000> + (-0.1233+0.1725i)|01001> + (0.0181+0.3166i)|01010> + (0.1150-0.1250i)|01011> + (-0.0050-0.0231i)|01100> + (0.0244-0.0367i)|01101> + (0.0002-0.0295i)|01110> + (-0.0386+0.0393i)|01111> + (-0.0680+0.1559i)|10000> + (-0.2972+0.1115i)|10001> + (0.1069-0.1830i)|10010> + (-0.3811+0.1063i)|10011> + (0.0200-0.0513i)|10100> + (0.0268-0.0123i)|10101> + (-0.0238+0.0372i)|10110> + (0.0232-0.0047i)|10111> + (-0.1832-0.0182i)|11000> + (-0.0637-0.0753i)|11001> + (-0.2816-0.1034i)|11010> + (0.0653+0.1468i)|11011> + (-0.0219-0.0043i)|11100> + (-0.0227-0.0350i)|11101> + (-0.0133-0.0035i)|11110> + (0.0133+0.0219i)|11111>\n  |10110> -> (0.0961-0.2357i)|00000> + (-0.1265+0.0509i)|00001> + (0.1681-0.2690i)|00010> + (0.1650-0.0408i)|00011> + (0.0574-0.1167i)|00100> + (-0.2285+0.0818i)|00101> + (0.0490-0.0921i)|00110> + (0.1870-0.0541i)|00111> + (-0.0589-0.0528i)|01000> + (0.0104+0.1473i)|01001> + (0.0982+0.0835i)|01010> + (0.0157+0.2401i)|01011> + (0.1515+0.1044i)|01100> + (-0.0164-0.0972i)|01101> + (-0.0761-0.0835i)|01110> + (0.0019-0.0605i)|01111> + (0.1667+0.1731i)|10000> + (0.0044-0.1287i)|10001> + (0.1035+0.1058i)|10010> + (0.0003+0.0793i)|10011> + (-0.0466-0.0389i)|10100> + (0.0119+0.1126i)|10101> + (-0.0608-0.0775i)|10110> + (0.0248-0.1822i)|10111> + (-0.1411+0.0949i)|11000> + (0.3124+0.0562i)|11001> + (0.1222-0.0601i)|11010> + (0.2394+0.0857i)|11011> + (-0.1650+0.1031i)|11100> + (0.1012+0.0250i)|11101> + (0.2141-0.1144i)|11110> + (0.1250+0.0359i)|11111>\n  |10111> -> (0.0167-0.0409i)|00000> + (-0.0219+0.0088i)|00001> + (0.0292-0.0467i)|00010> + (0.0286-0.0071i)|00011> + (-0.0935+0.1902i)|00100> + (0.3725-0.1333i)|00101> + (-0.0798+0.1501i)|00110> + (-0.3049+0.0881i)|00111> + (0.0102+0.0092i)|01000> + (-0.0018-0.0256i)|01001> + (-0.0170-0.0145i)|01010> + (-0.0027-0.0417i)|01011> + (0.2470+0.1702i)|01100> + (-0.0267-0.1585i)|01101> + (-0.1240-0.1361i)|01110> + (0.0030-0.0986i)|01111> + (0.0289+0.0300i)|10000> + (0.0008-0.0223i)|10001> + (0.0180+0.0184i)|10010> + (0.0001+0.0138i)|10011> + (0.0759+0.0633i)|10100> + (-0.0194-0.1835i)|10101> + (0.0991+0.1263i)|10110> + (-0.0405+0.2970i)|10111> + (0.0245-0.0165i)|11000> + (-0.0542-0.0097i)|11001> + (-0.0212+0.0104i)|11010> + (-0.0415-0.0149i)|11011> + (-0.2689+0.1681i)|11100> + (0.1649+0.0407i)|11101> + (0.3491-0.1865i)|11110> + (0.2038+0.0585i)|11111>\n  |11000> -> (-0.0252+0.0332i)|00000> + (0.0222-0.0027i)|00001> + (0.0200-0.0161i)|00010> + (0.0137+0.0012i)|00011> + (-0.0702+0.0696i)|00100> + (0.1846-0.0021i)|00101> + (0.1096-0.1173i)|00110> + (0.2997-0.0056i)|00111> + (-0.0258-0.0143i)|01000> + (0.0160+0.0527i)|01001> + (-0.0202-0.0122i)|01010> + (-0.0099-0.0430i)|01011> + (0.2867+0.1356i)|01100> + (-0.0548-0.1608i)|01101> + (0.3250+0.2259i)|01110> + (0.0407+0.2081i)|01111> + (0.0213+0.0387i)|10000> + (0.0069-0.0226i)|10001> + (-0.0235-0.0498i)|10010> + (0.0095-0.0279i)|10011> + (-0.1095-0.1814i)|10100> + (-0.0890+0.3855i)|10101> + (0.0666+0.1564i)|10110> + (-0.1231+0.2926i)|10111> + (0.0094-0.0100i)|11000> + (-0.0256+0.0012i)|11001> + (0.0182-0.0130i)|11010> + (0.0411+0.0076i)|11011> + (0.2255-0.1979i)|11100> + (-0.1602-0.0129i)|11101> + (0.1391-0.1207i)|11110> + (0.0985+0.0054i)|11111>\n  |11001> -> (0.1454-0.1913i)|00000> + (-0.1278+0.0154i)|00001> + (-0.1151+0.0931i)|00010> + (-0.0790-0.0071i)|00011> + (-0.0431+0.0427i)|00100> + (0.1132-0.0013i)|00101> + (0.0672-0.0720i)|00110> + (0.1838-0.0034i)|00111> + (-0.1487-0.0824i)|01000> + (0.0922+0.3037i)|01001> + (-0.1166-0.0704i)|01010> + (-0.0572-0.2478i)|01011> + (-0.1759-0.0832i)|01100> + (0.0336+0.0986i)|01101> + (-0.1994-0.1386i)|01110> + (-0.0250-0.1277i)|01111> + (-0.1229-0.2229i)|10000> + (-0.0399+0.1304i)|10001> + (0.1356+0.2868i)|10010> + (-0.0548+0.1609i)|10011> + (-0.0672-0.1113i)|10100> + (-0.0546+0.2365i)|10101> + (0.0409+0.0960i)|10110> + (-0.0755+0.1795i)|10111> + (0.0542-0.0576i)|11000> + (-0.1475+0.0068i)|11001> + (0.1050-0.0747i)|11010> + (0.2366+0.0435i)|11011> + (-0.1383+0.1214i)|11100> + (0.0983+0.0079i)|11101> + (-0.0853+0.0740i)|11110> + (-0.0604-0.0033i)|11111>\n  |11010> -> (-0.0936-0.1419i)|00000> + (0.0685-0.3099i)|00001> + (-0.0740-0.1986i)|00010> + (-0.1590+0.3623i)|00011> + (0.0270+0.0480i)|00100> + (-0.0075+0.0285i)|00101> + (0.0183+0.0402i)|00110> + (0.0086-0.0220i)|00111> + (-0.1788+0.0438i)|01000> + (-0.0851-0.0498i)|01001> + (0.2934-0.0626i)|01010> + (-0.1335-0.0895i)|01011> + (-0.0209+0.0080i)|01100> + (-0.0379-0.0175i)|01101> + (0.0137-0.0011i)|01110> + (-0.0198-0.0162i)|01111> + (0.1583-0.0266i)|10000> + (0.2414+0.1776i)|10001> + (0.0982-0.0117i)|10010> + (-0.1467-0.1119i)|10011> + (0.0247-0.0070i)|10100> + (0.0121+0.0065i)|10101> + (0.0417-0.0004i)|10110> + (-0.0157-0.0159i)|10111> + (-0.0032+0.3958i)|11000> + (-0.1488+0.1510i)|11001> + (0.0626-0.3109i)|11010> + (-0.1429+0.0919i)|11011> + (0.0010-0.0236i)|11100> + (0.0329-0.0294i)|11101> + (-0.0048+0.0291i)|11110> + (0.0443-0.0327i)|11111>\n  |11011> -> (0.0574+0.0871i)|00000> + (-0.0420+0.1901i)|00001> + (0.0454+0.1218i)|00010> + (0.0975-0.2222i)|00011> + (0.1558+0.2763i)|00100> + (-0.0431+0.1644i)|00101> + (0.1053+0.2317i)|00110> + (0.0498-0.1269i)|00111> + (-0.1097+0.0269i)|01000> + (-0.0522-0.0306i)|01001> + (0.1800-0.0384i)|01010> + (-0.0819-0.0549i)|01011> + (0.1203-0.0463i)|01100> + (0.2183+0.1011i)|01101> + (-0.0788+0.0066i)|01110> + (0.1142+0.0936i)|01111> + (-0.0971+0.0163i)|10000> + (-0.1481-0.1090i)|10001> + (-0.0602+0.0072i)|10010> + (0.0900+0.0687i)|10011> + (0.1424-0.0402i)|10100> + (0.0698+0.0377i)|10101> + (0.2403-0.0023i)|10110> + (-0.0905-0.0916i)|10111> + (-0.0020+0.2428i)|11000> + (-0.0913+0.0926i)|11001> + (0.0384-0.1907i)|11010> + (-0.0877+0.0564i)|11011> + (-0.0057+0.1361i)|11100> + (-0.1898+0.1693i)|11101> + (0.0279-0.1677i)|11110> + (-0.2554+0.1885i)|11111>\n  |11100> -> (0.0007+0.1288i)|00000> + (-0.1716+0.1683i)|00001> + (0.0227-0.0760i)|00010> + (-0.1292+0.0723i)|00011> + (-0.0151+0.1122i)|00100> + (-0.0477+0.0375i)|00101> + (0.0277-0.1818i)|00110> + (-0.0802+0.0571i)|00111> + (-0.3139+0.0473i)|01000> + (-0.1383-0.0989i)|01001> + (-0.2539+0.0145i)|01010> + (0.1003+0.0922i)|01011> + (0.1018-0.0221i)|01100> + (0.1620+0.1077i)|01101> + (0.1301+0.0009i)|01110> + (-0.1731-0.1703i)|01111> + (0.1250+0.0545i)|10000> + (0.0894+0.2383i)|10001> + (-0.1467-0.0857i)|10010> + (0.0852+0.3056i)|10011> + (-0.2261-0.0882i)|10100> + (-0.0541-0.1182i)|10101> + (0.1641+0.1047i)|10110> + (-0.0209-0.1022i)|10111> + (0.0146-0.1469i)|11000> + (0.0604-0.0511i)|11001> + (0.0829-0.2258i)|11010> + (-0.1178+0.0523i)|11011> + (0.0191-0.0967i)|11100> + (0.1544-0.1001i)|11101> + (0.0153-0.0585i)|11110> + (-0.0966+0.0586i)|11111>\n  |11101> -> (0.0001+0.0223i)|00000> + (-0.0298+0.0292i)|00001> + (0.0039-0.0132i)|00010> + (-0.0224+0.0125i)|00011> + (0.0246-0.1829i)|00100> + (0.0777-0.0612i)|00101> + (-0.0451+0.2963i)|00110> + (0.1308-0.0932i)|00111> + (0.0545-0.0082i)|01000> + (0.0240+0.0172i)|01001> + (0.0441-0.0025i)|01010> + (-0.0174-0.0160i)|01011> + (0.1660-0.0361i)|01100> + (0.2641+0.1756i)|01101> + (0.2120+0.0015i)|01110> + (-0.2821-0.2776i)|01111> + (0.0217+0.0095i)|10000> + (0.0155+0.0413i)|10001> + (-0.0255-0.0149i)|10010> + (0.0148+0.0530i)|10011> + (0.3686+0.1437i)|10100> + (0.0881+0.1927i)|10101> + (-0.2676-0.1707i)|10110> + (0.0341+0.1666i)|10111> + (-0.0025+0.0255i)|11000> + (-0.0105+0.0089i)|11001> + (-0.0144+0.0392i)|11010> + (0.0204-0.0091i)|11011> + (0.0311-0.1577i)|11100> + (0.2517-0.1632i)|11101> + (0.0249-0.0954i)|11110> + (-0.1574+0.0955i)|11111>\n  |11110> -> (0.1803+0.0735i)|00000> + (-0.0390-0.0967i)|00001> + (0.2058+0.1286i)|00010> + (0.0312+0.1262i)|00011> + (-0.1525-0.0750i)|00100> + (0.1069+0.2987i)|00101> + (-0.1204-0.0640i)|00110> + (-0.0707-0.2445i)|00111> + (0.0404-0.0451i)|01000> + (-0.1127+0.0080i)|01001> + (-0.0639+0.0751i)|01010> + (-0.1836+0.0120i)|01011> + (0.1365-0.1981i)|01100> + (-0.1271+0.0214i)|01101> + (-0.1091+0.0995i)|01110> + (-0.0791-0.0024i)|01111> + (-0.1324+0.1276i)|10000> + (0.0984+0.0033i)|10001> + (-0.0810+0.0791i)|10010> + (-0.0607+0.0002i)|10011> + (-0.0508+0.0609i)|10100> + (0.1472-0.0156i)|10101> + (-0.1013+0.0795i)|10110> + (-0.2381-0.0325i)|10111> + (-0.0726-0.1079i)|11000> + (-0.0430+0.2390i)|11001> + (0.0460+0.0935i)|11010> + (-0.0655+0.1832i)|11011> + (0.1348+0.2157i)|11100> + (0.0327-0.1323i)|11101> + (-0.1496-0.2799i)|11110> + (0.0469-0.1634i)|11111>\n  |11111> -> (0.2939+0.1198i)|00000> + (-0.0635-0.1577i)|00001> + (0.3355+0.2097i)|00010> + (0.0508+0.2057i)|00011> + (0.0265+0.0130i)|00100> + (-0.0185-0.0518i)|00101> + (0.0209+0.0111i)|00110> + (0.0123+0.0424i)|00111> + (-0.0658+0.0735i)|01000> + (0.1837-0.0130i)|01001> + (0.1041-0.1224i)|01010> + (0.2993-0.0195i)|01011> + (0.0237-0.0344i)|01100> + (-0.0221+0.0037i)|01101> + (-0.0189+0.0173i)|01110> + (-0.0137-0.0004i)|01111> + (-0.2158+0.2079i)|10000> + (0.1605+0.0055i)|10001> + (-0.1320+0.1290i)|10010> + (-0.0989+0.0004i)|10011> + (0.0088-0.0106i)|10100> + (-0.0255+0.0027i)|10101> + (0.0176-0.0138i)|10110> + (0.0413+0.0056i)|10111> + (0.1184+0.1759i)|11000> + (0.0700-0.3896i)|11001> + (-0.0750-0.1524i)|11010> + (0.1068-0.2986i)|11011> + (0.0234+0.0374i)|11100> + (0.0057-0.0229i)|11101> + (-0.0260-0.0486i)|11110> + (0.0081-0.0284i)|11111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "The following 5-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\ns q[2];\nh q[2];\nz q[3];\ny q[4];\nh q[0];\ns q[3];\ncx q[2],q[3];\nh q[3];\ns q[4];\nx q[4];\nz q[1];\ny q[3];\nx q[2];\nx q[0];\ncz q[3],q[0];\nh q[1];\ncx q[3],q[1];\ny q[4];\ny q[2];\nt q[3];\nrx(3.683410660595319) q[4];\ny q[0];\ns q[1];\ncz q[3],q[1];\ncz q[0],q[2];\ns q[2];\ncz q[2],q[1];\ns q[1];\nx q[2];\nrx(4.041467099982676) q[3];\nz q[3];\nh q[4];\ncz q[1],q[2];\ncx q[0],q[2];\nh q[3];\nrx(1.0261827657685991) q[0];\ncx q[2],q[1];\nz q[2];\ncx q[0],q[2];\ncx q[1],q[2];\ncz q[3],q[1];\ny q[2];\ny q[1];\ncx q[1],q[0];\nz q[2];\nx q[1];\nry(2.3582214925279765) q[0];\ncz q[0],q[1];\nz q[0];\nx q[1];\nry(1.3121359422204464) q[4];\ncz q[4],q[3];\ns q[0];\ncz q[0],q[2];\ncz q[4],q[2];\nry(5.53552859813581) q[3];\nry(4.521332379384323) q[4];\nrz(5.517730087703933) q[4];\ncx q[0],q[1];\nz q[1];\nx q[4];\nx q[2];\nh q[4];\nx q[1];\nrz(1.2059350174978194) q[2];\ncx q[3],q[4];\ny q[3];\nh q[1];\ncx q[0],q[3];\nh q[0];\ny q[2];\nh q[3];\nh q[3];\ncz q[0],q[1];\nz q[1];\ny q[2];\ncx q[3],q[4];\nry(6.0868567274801775) q[2];\ny q[1];\nh q[4];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00000> -> (-0.1737-0.1167i)|00000> + (0.1008-0.1802i)|00001> + (-0.1643-0.0798i)|00010> + (0.0438+0.1126i)|00011> + (-0.0952+0.0937i)|00100> + (-0.0329-0.0049i)|00101> + (-0.0614-0.0653i)|00110> + (0.0022+0.2221i)|00111> + (-0.1565-0.1515i)|01000> + (-0.0804+0.0824i)|01001> + (0.1051-0.0123i)|01010> + (0.0916-0.0449i)|01011> + (0.1085-0.0291i)|01100> + (-0.0406-0.1742i)|01101> + (-0.0252-0.0476i)|01110> + (-0.0055-0.2843i)|01111> + (0.2941-0.1346i)|10000> + (0.0195-0.0775i)|10001> + (0.1506-0.1434i)|10010> + (0.1020+0.1193i)|10011> + (-0.1222-0.0137i)|10100> + (-0.1325-0.0315i)|10101> + (0.1267-0.0823i)|10110> + (0.0887+0.2147i)|10111> + (-0.2327+0.0970i)|11000> + (0.0435-0.1315i)|11001> + (-0.0245-0.0243i)|11010> + (-0.1294-0.0616i)|11011> + (0.0336-0.1416i)|11100> + (0.1339+0.1509i)|11101> + (-0.2057+0.1694i)|11110> + (0.1123+0.1982i)|11111>\n  |00001> -> (-0.0449-0.0916i)|00000> + (-0.0123-0.1051i)|00001> + (0.0824+0.0804i)|00010> + (-0.1515+0.1565i)|00011> + (-0.2843+0.0055i)|00100> + (-0.0476+0.0252i)|00101> + (-0.1742+0.0406i)|00110> + (-0.0291-0.1085i)|00111> + (0.1126-0.0438i)|01000> + (-0.0798+0.1643i)|01001> + (-0.1802-0.1008i)|01010> + (-0.1167+0.1737i)|01011> + (0.2221-0.0022i)|01100> + (-0.0653+0.0614i)|01101> + (-0.0049+0.0329i)|01110> + (0.0937+0.0952i)|01111> + (0.0616-0.1294i)|10000> + (0.0243-0.0245i)|10001> + (0.1315+0.0435i)|10010> + (-0.0970-0.2327i)|10011> + (-0.1982+0.1123i)|10100> + (-0.1694-0.2057i)|10101> + (-0.1509+0.1339i)|10110> + (0.1416+0.0336i)|10111> + (-0.1193+0.1020i)|11000> + (0.1434+0.1506i)|11001> + (0.0775+0.0195i)|11010> + (0.1346+0.2941i)|11011> + (-0.2147+0.0887i)|11100> + (0.0823+0.1267i)|11101> + (0.0315-0.1325i)|11110> + (0.0137-0.1222i)|11111>\n  |00010> -> (-0.0394+0.0910i)|00000> + (0.1828+0.0280i)|00001> + (-0.0325-0.2352i)|00010> + (0.1820+0.0295i)|00011> + (0.0187+0.1953i)|00100> + (0.0413-0.1454i)|00101> + (0.0497-0.0234i)|00110> + (0.0974+0.0498i)|00111> + (0.0446+0.0871i)|01000> + (0.1068+0.0676i)|01001> + (-0.0591-0.1398i)|01010> + (-0.1833+0.0114i)|01011> + (0.0458+0.2528i)|01100> + (-0.0169+0.1161i)|01101> + (-0.0350+0.1915i)|01110> + (0.1019-0.0180i)|01111> + (0.0914+0.1040i)|10000> + (-0.1984+0.0633i)|10001> + (-0.1439+0.0091i)|10010> + (-0.2452+0.1881i)|10011> + (0.2049+0.0422i)|10100> + (-0.0166+0.1951i)|10101> + (-0.0743-0.1194i)|10110> + (-0.0015-0.0926i)|10111> + (-0.0074+0.1427i)|11000> + (0.0514+0.0633i)|11001> + (0.1681+0.0049i)|11010> + (-0.1839+0.1238i)|11011> + (-0.1686-0.0894i)|11100> + (-0.0905+0.2702i)|11101> + (-0.1813-0.1200i)|11110> + (0.1148-0.0824i)|11111>\n  |00011> -> (-0.0114-0.1833i)|00000> + (0.1398-0.0591i)|00001> + (-0.0676+0.1068i)|00010> + (-0.0871+0.0446i)|00011> + (0.0180+0.1019i)|00100> + (-0.1915-0.0350i)|00101> + (-0.1161-0.0169i)|00110> + (-0.2528+0.0458i)|00111> + (-0.0295+0.1820i)|01000> + (0.2352-0.0325i)|01001> + (-0.0280+0.1828i)|01010> + (-0.0910-0.0394i)|01011> + (-0.0498+0.0974i)|01100> + (0.0234+0.0497i)|01101> + (0.1454+0.0413i)|01110> + (-0.1953+0.0187i)|01111> + (0.1238+0.1839i)|10000> + (0.0049-0.1681i)|10001> + (0.0633-0.0514i)|10010> + (0.1427+0.0074i)|10011> + (-0.0824-0.1148i)|10100> + (-0.1200+0.1813i)|10101> + (0.2702+0.0905i)|10110> + (-0.0894+0.1686i)|10111> + (0.1881+0.2452i)|11000> + (0.0091+0.1439i)|11001> + (0.0633+0.1984i)|11010> + (0.1040-0.0914i)|11011> + (-0.0926+0.0015i)|11100> + (-0.1194+0.0743i)|11101> + (0.1951+0.0166i)|11110> + (0.0422-0.2049i)|11111>\n  |00100> -> (-0.2037-0.0691i)|00000> + (-0.1467+0.1144i)|00001> + (-0.2032-0.0704i)|00010> + (0.0060-0.0346i)|00011> + (-0.0064-0.0116i)|00100> + (0.0749-0.1366i)|00101> + (-0.2106+0.0427i)|00110> + (0.0854+0.0664i)|00111> + (0.1639+0.1032i)|01000> + (-0.1370+0.0628i)|01001> + (-0.0759-0.0294i)|01010> + (0.0833-0.0504i)|01011> + (-0.1883-0.0277i)|01100> + (-0.0129+0.0933i)|01101> + (0.2907-0.0529i)|01110> + (0.0425+0.0106i)|01111> + (-0.0433-0.0540i)|10000> + (-0.2005-0.2777i)|10001> + (0.0822-0.0150i)|10010> + (0.0895+0.2185i)|10011> + (0.1241-0.0209i)|10100> + (-0.0699-0.0430i)|10101> + (-0.1603-0.0224i)|10110> + (0.1572+0.1761i)|10111> + (-0.0057-0.1190i)|11000> + (0.1271+0.2174i)|11001> + (-0.1778+0.0003i)|11010> + (-0.0147+0.0323i)|11011> + (-0.0024-0.0175i)|11100> + (-0.1757-0.1894i)|11101> + (-0.1842+0.0511i)|11110> + (-0.2090-0.1778i)|11111>\n  |00101> -> (-0.0504-0.0833i)|00000> + (-0.0294+0.0759i)|00001> + (0.0628+0.1370i)|00010> + (0.1032-0.1639i)|00011> + (0.0106-0.0425i)|00100> + (-0.0529-0.2907i)|00101> + (0.0933+0.0129i)|00110> + (-0.0277+0.1883i)|00111> + (-0.0346-0.0060i)|01000> + (-0.0704+0.2032i)|01001> + (0.1144+0.1467i)|01010> + (-0.0691+0.2037i)|01011> + (0.0664-0.0854i)|01100> + (0.0427+0.2106i)|01101> + (-0.1366-0.0749i)|01110> + (-0.0116+0.0064i)|01111> + (-0.0323-0.0147i)|10000> + (-0.0003-0.1778i)|10001> + (-0.2174+0.1271i)|10010> + (0.1190-0.0057i)|10011> + (0.1778-0.2090i)|10100> + (-0.0511-0.1842i)|10101> + (0.1894-0.1757i)|10110> + (0.0175-0.0024i)|10111> + (-0.2185+0.0895i)|11000> + (0.0150+0.0822i)|11001> + (0.2777-0.2005i)|11010> + (0.0540-0.0433i)|11011> + (-0.1761+0.1572i)|11100> + (0.0224-0.1603i)|11101> + (0.0430-0.0699i)|11110> + (0.0209+0.1241i)|11111>\n  |00110> -> (-0.0560+0.0054i)|00000> + (-0.2056-0.0174i)|00001> + (-0.0038-0.1541i)|00010> + (-0.2425-0.0080i)|00011> + (0.1351-0.0846i)|00100> + (-0.1833+0.0242i)|00101> + (0.0731+0.1190i)|00110> + (-0.0135+0.0549i)|00111> + (-0.0771-0.0848i)|01000> + (0.0515+0.0451i)|01001> + (0.0380+0.0931i)|01010> + (-0.2199+0.0022i)|01011> + (-0.1120+0.0368i)|01100> + (-0.2712-0.0064i)|01101> + (-0.0051+0.0763i)|01110> + (0.1891-0.0725i)|01111> + (-0.1865-0.1600i)|10000> + (0.0703-0.0329i)|10001> + (0.1509+0.2845i)|10010> + (0.0547+0.1082i)|10011> + (-0.2405-0.0944i)|10100> + (0.0245+0.1044i)|10101> + (0.0529+0.0434i)|10110> + (-0.0285-0.1441i)|10111> + (0.0451+0.0134i)|11000> + (0.0695-0.1488i)|11001> + (0.1226+0.1962i)|11010> + (-0.1321-0.1016i)|11011> + (-0.2622-0.1456i)|11100> + (0.0282-0.1573i)|11101> + (-0.2132-0.1247i)|11110> + (-0.0458-0.0164i)|11111>\n  |00111> -> (-0.0022-0.2199i)|00000> + (-0.0931+0.0380i)|00001> + (-0.0451+0.0515i)|00010> + (0.0848-0.0771i)|00011> + (0.0725+0.1891i)|00100> + (-0.0763-0.0051i)|00101> + (0.0064-0.2712i)|00110> + (-0.0368-0.1120i)|00111> + (0.0080-0.2425i)|01000> + (0.1541-0.0038i)|01001> + (0.0174-0.2056i)|01010> + (-0.0054-0.0560i)|01011> + (-0.0549-0.0135i)|01100> + (-0.1190+0.0731i)|01101> + (-0.0242-0.1833i)|01110> + (0.0846+0.1351i)|01111> + (-0.1016+0.1321i)|10000> + (0.1962-0.1226i)|10001> + (-0.1488-0.0695i)|10010> + (0.0134-0.0451i)|10011> + (-0.0164+0.0458i)|10100> + (-0.1247+0.2132i)|10101> + (-0.1573-0.0282i)|10110> + (-0.1456+0.2622i)|10111> + (0.1082-0.0547i)|11000> + (0.2845-0.1509i)|11001> + (-0.0329-0.0703i)|11010> + (-0.1600+0.1865i)|11011> + (-0.1441+0.0285i)|11100> + (0.0434-0.0529i)|11101> + (0.1044-0.0245i)|11110> + (-0.0944+0.2405i)|11111>\n  |01000> -> (-0.0848+0.0771i)|00000> + (-0.0451+0.0515i)|00001> + (-0.0931+0.0380i)|00010> + (0.0022+0.2199i)|00011> + (0.0368+0.1120i)|00100> + (0.0064-0.2712i)|00101> + (-0.0763-0.0051i)|00110> + (-0.0725-0.1891i)|00111> + (0.0054+0.0560i)|01000> + (0.0174-0.2056i)|01001> + (0.1541-0.0038i)|01010> + (-0.0080+0.2425i)|01011> + (-0.0846-0.1351i)|01100> + (-0.0242-0.1833i)|01101> + (-0.1190+0.0731i)|01110> + (0.0549+0.0135i)|01111> + (-0.0134+0.0451i)|10000> + (-0.1488-0.0695i)|10001> + (0.1962-0.1226i)|10010> + (0.1016-0.1321i)|10011> + (0.1456-0.2622i)|10100> + (-0.1573-0.0282i)|10101> + (-0.1247+0.2132i)|10110> + (0.0164-0.0458i)|10111> + (0.1600-0.1865i)|11000> + (-0.0329-0.0703i)|11001> + (0.2845-0.1509i)|11010> + (-0.1082+0.0547i)|11011> + (0.0944-0.2405i)|11100> + (0.1044-0.0245i)|11101> + (0.0434-0.0529i)|11110> + (0.1441-0.0285i)|11111>\n  |01001> -> (0.2425+0.0080i)|00000> + (-0.0038-0.1541i)|00001> + (-0.2056-0.0174i)|00010> + (0.0560-0.0054i)|00011> + (0.0135-0.0549i)|00100> + (0.0731+0.1190i)|00101> + (-0.1833+0.0242i)|00110> + (-0.1351+0.0846i)|00111> + (0.2199-0.0022i)|01000> + (0.0380+0.0931i)|01001> + (0.0515+0.0451i)|01010> + (0.0771+0.0848i)|01011> + (-0.1891+0.0725i)|01100> + (-0.0051+0.0763i)|01101> + (-0.2712-0.0064i)|01110> + (0.1120-0.0368i)|01111> + (-0.0547-0.1082i)|10000> + (0.1509+0.2845i)|10001> + (0.0703-0.0329i)|10010> + (0.1865+0.1600i)|10011> + (0.0285+0.1441i)|10100> + (0.0529+0.0434i)|10101> + (0.0245+0.1044i)|10110> + (0.2405+0.0944i)|10111> + (0.1321+0.1016i)|11000> + (0.1226+0.1962i)|11001> + (0.0695-0.1488i)|11010> + (-0.0451-0.0134i)|11011> + (0.0458+0.0164i)|11100> + (-0.2132-0.1247i)|11101> + (0.0282-0.1573i)|11110> + (0.2622+0.1456i)|11111>\n  |01010> -> (-0.1032+0.1639i)|00000> + (0.0628+0.1370i)|00001> + (-0.0294+0.0759i)|00010> + (0.0504+0.0833i)|00011> + (0.0277-0.1883i)|00100> + (0.0933+0.0129i)|00101> + (-0.0529-0.2907i)|00110> + (-0.0106+0.0425i)|00111> + (0.0691-0.2037i)|01000> + (0.1144+0.1467i)|01001> + (-0.0704+0.2032i)|01010> + (0.0346+0.0060i)|01011> + (0.0116-0.0064i)|01100> + (-0.1366-0.0749i)|01101> + (0.0427+0.2106i)|01110> + (-0.0664+0.0854i)|01111> + (-0.1190+0.0057i)|10000> + (-0.2174+0.1271i)|10001> + (-0.0003-0.1778i)|10010> + (0.0323+0.0147i)|10011> + (-0.0175+0.0024i)|10100> + (0.1894-0.1757i)|10101> + (-0.0511-0.1842i)|10110> + (-0.1778+0.2090i)|10111> + (-0.0540+0.0433i)|11000> + (0.2777-0.2005i)|11001> + (0.0150+0.0822i)|11010> + (0.2185-0.0895i)|11011> + (-0.0209-0.1241i)|11100> + (0.0430-0.0699i)|11101> + (0.0224-0.1603i)|11110> + (0.1761-0.1572i)|11111>\n  |01011> -> (-0.0060+0.0346i)|00000> + (-0.2032-0.0704i)|00001> + (-0.1467+0.1144i)|00010> + (0.2037+0.0691i)|00011> + (-0.0854-0.0664i)|00100> + (-0.2106+0.0427i)|00101> + (0.0749-0.1366i)|00110> + (0.0064+0.0116i)|00111> + (-0.0833+0.0504i)|01000> + (-0.0759-0.0294i)|01001> + (-0.1370+0.0628i)|01010> + (-0.1639-0.1032i)|01011> + (-0.0425-0.0106i)|01100> + (0.2907-0.0529i)|01101> + (-0.0129+0.0933i)|01110> + (0.1883+0.0277i)|01111> + (-0.0895-0.2185i)|10000> + (0.0822-0.0150i)|10001> + (-0.2005-0.2777i)|10010> + (0.0433+0.0540i)|10011> + (-0.1572-0.1761i)|10100> + (-0.1603-0.0224i)|10101> + (-0.0699-0.0430i)|10110> + (-0.1241+0.0209i)|10111> + (0.0147-0.0323i)|11000> + (-0.1778+0.0003i)|11001> + (0.1271+0.2174i)|11010> + (0.0057+0.1190i)|11011> + (0.2090+0.1778i)|11100> + (-0.1842+0.0511i)|11101> + (-0.1757-0.1894i)|11110> + (0.0024+0.0175i)|11111>\n  |01100> -> (-0.0871+0.0446i)|00000> + (0.0676-0.1068i)|00001> + (-0.1398+0.0591i)|00010> + (-0.0114-0.1833i)|00011> + (-0.2528+0.0458i)|00100> + (0.1161+0.0169i)|00101> + (0.1915+0.0350i)|00110> + (0.0180+0.1019i)|00111> + (-0.0910-0.0394i)|01000> + (0.0280-0.1828i)|01001> + (-0.2352+0.0325i)|01010> + (-0.0295+0.1820i)|01011> + (-0.1953+0.0187i)|01100> + (-0.1454-0.0413i)|01101> + (-0.0234-0.0497i)|01110> + (-0.0498+0.0974i)|01111> + (0.1427+0.0074i)|10000> + (-0.0633+0.0514i)|10001> + (-0.0049+0.1681i)|10010> + (0.1238+0.1839i)|10011> + (-0.0894+0.1686i)|10100> + (-0.2702-0.0905i)|10101> + (0.1200-0.1813i)|10110> + (-0.0824-0.1148i)|10111> + (0.1040-0.0914i)|11000> + (-0.0633-0.1984i)|11001> + (-0.0091-0.1439i)|11010> + (0.1881+0.2452i)|11011> + (0.0422-0.2049i)|11100> + (-0.1951-0.0166i)|11101> + (0.1194-0.0743i)|11110> + (-0.0926+0.0015i)|11111>\n  |01101> -> (0.1820+0.0295i)|00000> + (0.0325+0.2352i)|00001> + (-0.1828-0.0280i)|00010> + (-0.0394+0.0910i)|00011> + (0.0974+0.0498i)|00100> + (-0.0497+0.0234i)|00101> + (-0.0413+0.1454i)|00110> + (0.0187+0.1953i)|00111> + (-0.1833+0.0114i)|01000> + (0.0591+0.1398i)|01001> + (-0.1068-0.0676i)|01010> + (0.0446+0.0871i)|01011> + (0.1019-0.0180i)|01100> + (0.0350-0.1915i)|01101> + (0.0169-0.1161i)|01110> + (0.0458+0.2528i)|01111> + (-0.2452+0.1881i)|10000> + (0.1439-0.0091i)|10001> + (0.1984-0.0633i)|10010> + (0.0914+0.1040i)|10011> + (-0.0015-0.0926i)|10100> + (0.0743+0.1194i)|10101> + (0.0166-0.1951i)|10110> + (0.2049+0.0422i)|10111> + (-0.1839+0.1238i)|11000> + (-0.1681-0.0049i)|11001> + (-0.0514-0.0633i)|11010> + (-0.0074+0.1427i)|11011> + (0.1148-0.0824i)|11100> + (0.1813+0.1200i)|11101> + (0.0905-0.2702i)|11110> + (-0.1686-0.0894i)|11111>\n  |01110> -> (-0.1515+0.1565i)|00000> + (-0.0824-0.0804i)|00001> + (0.0123+0.1051i)|00010> + (-0.0449-0.0916i)|00011> + (-0.0291-0.1085i)|00100> + (0.1742-0.0406i)|00101> + (0.0476-0.0252i)|00110> + (-0.2843+0.0055i)|00111> + (-0.1167+0.1737i)|01000> + (0.1802+0.1008i)|01001> + (0.0798-0.1643i)|01010> + (0.1126-0.0438i)|01011> + (0.0937+0.0952i)|01100> + (0.0049-0.0329i)|01101> + (0.0653-0.0614i)|01110> + (0.2221-0.0022i)|01111> + (-0.0970-0.2327i)|10000> + (-0.1315-0.0435i)|10001> + (-0.0243+0.0245i)|10010> + (0.0616-0.1294i)|10011> + (0.1416+0.0336i)|10100> + (0.1509-0.1339i)|10101> + (0.1694+0.2057i)|10110> + (-0.1982+0.1123i)|10111> + (0.1346+0.2941i)|11000> + (-0.0775-0.0195i)|11001> + (-0.1434-0.1506i)|11010> + (-0.1193+0.1020i)|11011> + (0.0137-0.1222i)|11100> + (-0.0315+0.1325i)|11101> + (-0.0823-0.1267i)|11110> + (-0.2147+0.0887i)|11111>\n  |01111> -> (0.0438+0.1126i)|00000> + (0.1643+0.0798i)|00001> + (-0.1008+0.1802i)|00010> + (-0.1737-0.1167i)|00011> + (0.0022+0.2221i)|00100> + (0.0614+0.0653i)|00101> + (0.0329+0.0049i)|00110> + (-0.0952+0.0937i)|00111> + (0.0916-0.0449i)|01000> + (-0.1051+0.0123i)|01001> + (0.0804-0.0824i)|01010> + (-0.1565-0.1515i)|01011> + (-0.0055-0.2843i)|01100> + (0.0252+0.0476i)|01101> + (0.0406+0.1742i)|01110> + (0.1085-0.0291i)|01111> + (0.1020+0.1193i)|10000> + (-0.1506+0.1434i)|10001> + (-0.0195+0.0775i)|10010> + (0.2941-0.1346i)|10011> + (0.0887+0.2147i)|10100> + (-0.1267+0.0823i)|10101> + (0.1325+0.0315i)|10110> + (-0.1222-0.0137i)|10111> + (-0.1294-0.0616i)|11000> + (0.0245+0.0243i)|11001> + (-0.0435+0.1315i)|11010> + (-0.2327+0.0970i)|11011> + (0.1123+0.1982i)|11100> + (0.2057-0.1694i)|11101> + (-0.1339-0.1509i)|11110> + (0.0336-0.1416i)|11111>\n  |10000> -> (-0.2602+0.0319i)|00000> + (0.0689+0.1890i)|00001> + (-0.0761-0.0936i)|00010> + (0.0123-0.1854i)|00011> + (0.0516+0.0288i)|00100> + (0.0352-0.1753i)|00101> + (0.2528-0.0792i)|00110> + (0.1237+0.1003i)|00111> + (-0.1855+0.0318i)|01000> + (-0.0897-0.2409i)|01001> + (-0.0161+0.0723i)|01010> + (0.0567-0.1218i)|01011> + (-0.1751-0.0012i)|01100> + (0.0054-0.1116i)|01101> + (0.3123-0.1293i)|01110> + (-0.0812-0.0176i)|01111> + (-0.0318-0.0377i)|10000> + (0.2122+0.1945i)|10001> + (0.0948-0.0126i)|10010> + (-0.0702-0.1487i)|10011> + (-0.0783+0.0744i)|10100> + (0.0562-0.0724i)|10101> + (-0.0224+0.2246i)|10110> + (0.1314+0.0310i)|10111> + (-0.0090+0.1215i)|11000> + (0.1620+0.1772i)|11001> + (0.1388-0.0411i)|11010> + (0.0194+0.0371i)|11011> + (-0.0592+0.1518i)|11100> + (0.0174+0.0775i)|11101> + (0.0135-0.2011i)|11110> + (0.1987+0.0499i)|11111>\n  |10001> -> (-0.1218-0.0567i)|00000> + (0.0723+0.0161i)|00001> + (-0.2409+0.0897i)|00010> + (0.0318+0.1855i)|00011> + (-0.0176+0.0812i)|00100> + (-0.1293-0.3123i)|00101> + (-0.1116-0.0054i)|00110> + (-0.0012+0.1751i)|00111> + (-0.1854-0.0123i)|01000> + (-0.0936+0.0761i)|01001> + (0.1890-0.0689i)|01010> + (0.0319+0.2602i)|01011> + (0.1003-0.1237i)|01100> + (-0.0792-0.2528i)|01101> + (-0.1753-0.0352i)|01110> + (0.0288-0.0516i)|01111> + (-0.0371+0.0194i)|10000> + (0.0411+0.1388i)|10001> + (-0.1772+0.1620i)|10010> + (-0.1215-0.0090i)|10011> + (-0.0499+0.1987i)|10100> + (0.2011+0.0135i)|10101> + (-0.0775+0.0174i)|10110> + (-0.1518-0.0592i)|10111> + (0.1487-0.0702i)|11000> + (0.0126+0.0948i)|11001> + (-0.1945+0.2122i)|11010> + (0.0377-0.0318i)|11011> + (-0.0310+0.1314i)|11100> + (-0.2246-0.0224i)|11101> + (0.0724+0.0562i)|11110> + (-0.0744-0.0783i)|11111>\n  |10010> -> (0.0200-0.1851i)|00000> + (0.0943-0.0141i)|00001> + (-0.0756+0.1602i)|00010> + (0.2518+0.1404i)|00011> + (-0.1216+0.1615i)|00100> + (-0.2406+0.0461i)|00101> + (-0.0932-0.1294i)|00110> + (-0.0415+0.0548i)|00111> + (0.0102+0.1530i)|01000> + (-0.0034-0.0731i)|01001> + (-0.1111+0.1983i)|01010> + (-0.1829-0.1052i)|01011> + (-0.1124+0.0668i)|01100> + (0.3131-0.0266i)|01101> + (0.0311+0.1014i)|01110> + (-0.1523+0.1183i)|01111> + (-0.1459-0.0811i)|10000> + (-0.0563+0.0345i)|10001> + (0.1495+0.2253i)|10010> + (-0.0868-0.0928i)|10011> + (0.0872+0.1595i)|10100> + (0.1516-0.1308i)|10101> + (0.0009+0.0502i)|10110> + (0.0456-0.1073i)|10111> + (-0.0786-0.0187i)|11000> + (0.0541-0.1312i)|11001> + (-0.1404-0.1555i)|11010> + (-0.1508-0.0432i)|11011> + (-0.1305-0.1892i)|11100> + (0.0992-0.1264i)|11101> + (-0.0660-0.0063i)|11110> + (-0.0816+0.1605i)|11111>\n  |10011> -> (0.1052-0.1829i)|00000> + (-0.1983-0.1111i)|00001> + (0.0731-0.0034i)|00010> + (-0.1530+0.0102i)|00011> + (-0.1183-0.1523i)|00100> + (-0.1014+0.0311i)|00101> + (0.0266+0.3131i)|00110> + (-0.0668-0.1124i)|00111> + (-0.1404+0.2518i)|01000> + (-0.1602-0.0756i)|01001> + (0.0141+0.0943i)|01010> + (0.1851+0.0200i)|01011> + (-0.0548-0.0415i)|01100> + (0.1294-0.0932i)|01101> + (-0.0461-0.2406i)|01110> + (-0.1615-0.1216i)|01111> + (-0.0432+0.1508i)|10000> + (-0.1555+0.1404i)|10001> + (-0.1312-0.0541i)|10010> + (-0.0187+0.0786i)|10011> + (0.1605+0.0816i)|10100> + (-0.0063+0.0660i)|10101> + (-0.1264-0.0992i)|10110> + (-0.1892+0.1305i)|10111> + (-0.0928+0.0868i)|11000> + (0.2253-0.1495i)|11001> + (0.0345+0.0563i)|11010> + (-0.0811+0.1459i)|11011> + (-0.1073-0.0456i)|11100> + (0.0502-0.0009i)|11101> + (-0.1308-0.1516i)|11110> + (0.1595-0.0872i)|11111>\n  |10100> -> (0.1877-0.1167i)|00000> + (-0.0281+0.2658i)|00001> + (0.0261+0.0310i)|00010> + (0.0030-0.2057i)|00011> + (0.0910-0.1047i)|00100> + (-0.0283-0.0655i)|00101> + (0.0765+0.0837i)|00110> + (0.0646+0.2893i)|00111> + (-0.0822+0.1174i)|01000> + (0.0310+0.2737i)|01001> + (-0.1020+0.0582i)|01010> + (-0.0080+0.1442i)|01011> + (0.0864-0.0718i)|01100> + (0.0868+0.1676i)|01101> + (0.0125-0.0817i)|01110> + (0.0573+0.3161i)|01111> + (0.2319-0.1505i)|10000> + (-0.0406+0.0413i)|10001> + (0.1030-0.1130i)|10010> + (-0.1013-0.0455i)|10011> + (-0.0796+0.1058i)|10100> + (-0.0883+0.0155i)|10101> + (-0.0643+0.2150i)|10110> + (-0.1240+0.0625i)|10111> + (0.1940-0.1541i)|11000> + (0.0188-0.1013i)|11001> + (-0.0149+0.0501i)|11010> + (-0.1107-0.0472i)|11011> + (0.0572-0.1666i)|11100> + (0.0255+0.0408i)|11101> + (-0.0940+0.1867i)|11110> + (0.2103-0.0139i)|11111>\n  |10101> -> (0.1442+0.0080i)|00000> + (0.0582+0.1020i)|00001> + (0.2737-0.0310i)|00010> + (0.1174+0.0822i)|00011> + (0.3161-0.0573i)|00100> + (-0.0817-0.0125i)|00101> + (0.1676-0.0868i)|00110> + (-0.0718-0.0864i)|00111> + (-0.2057-0.0030i)|01000> + (0.0310-0.0261i)|01001> + (0.2658+0.0281i)|01010> + (-0.1167-0.1877i)|01011> + (0.2893-0.0646i)|01100> + (0.0837-0.0765i)|01101> + (-0.0655+0.0283i)|01110> + (-0.1047-0.0910i)|01111> + (0.0472-0.1107i)|10000> + (-0.0501-0.0149i)|10001> + (0.1013+0.0188i)|10010> + (0.1541+0.1940i)|10011> + (0.0139+0.2103i)|10100> + (-0.1867-0.0940i)|10101> + (-0.0408+0.0255i)|10110> + (0.1666+0.0572i)|10111> + (0.0455-0.1013i)|11000> + (0.1130+0.1030i)|11001> + (-0.0413-0.0406i)|11010> + (0.1505+0.2319i)|11011> + (-0.0625-0.1240i)|11100> + (-0.2150-0.0643i)|11101> + (-0.0155-0.0883i)|11110> + (-0.1058-0.0796i)|11111>\n  |10110> -> (-0.0715+0.1904i)|00000> + (0.0246-0.0753i)|00001> + (0.0765-0.2748i)|00010> + (0.1587+0.1005i)|00011> + (-0.0388-0.2677i)|00100> + (0.0171-0.1535i)|00101> + (-0.0380+0.0968i)|00110> + (0.1258+0.0372i)|00111> + (0.0119+0.1268i)|01000> + (0.0728+0.0972i)|01001> + (-0.1049+0.2800i)|01010> + (0.0412+0.0946i)|01011> + (0.0940+0.2887i)|01100> + (-0.0531-0.1368i)|01101> + (0.0018+0.1941i)|01110> + (-0.0826+0.0081i)|01111> + (0.0641+0.0675i)|10000> + (0.1508-0.0508i)|10001> + (-0.1021+0.0745i)|10010> + (0.1828-0.1792i)|10011> + (0.0270+0.0811i)|10100> + (-0.1901+0.1671i)|10101> + (0.0258+0.1019i)|10110> + (-0.0410+0.1053i)|10111> + (-0.0111-0.1115i)|11000> + (0.0798-0.0058i)|11001> + (-0.1439+0.0280i)|11010> + (-0.1698+0.1411i)|11011> + (0.1105+0.1360i)|11100> + (0.1532-0.1794i)|11101> + (0.0729-0.0421i)|11110> + (-0.1020+0.1327i)|11111>\n  |10111> -> (-0.0946+0.0412i)|00000> + (-0.2800-0.1049i)|00001> + (-0.0972+0.0728i)|00010> + (-0.1268+0.0119i)|00011> + (-0.0081-0.0826i)|00100> + (-0.1941+0.0018i)|00101> + (0.1368-0.0531i)|00110> + (-0.2887+0.0940i)|00111> + (-0.1005+0.1587i)|01000> + (0.2748+0.0765i)|01001> + (0.0753+0.0246i)|01010> + (-0.1904-0.0715i)|01011> + (-0.0372+0.1258i)|01100> + (-0.0968-0.0380i)|01101> + (0.1535+0.0171i)|01110> + (0.2677-0.0388i)|01111> + (0.1411+0.1698i)|10000> + (0.0280+0.1439i)|10001> + (-0.0058-0.0798i)|10010> + (-0.1115+0.0111i)|10011> + (0.1327+0.1020i)|10100> + (-0.0421-0.0729i)|10101> + (-0.1794-0.1532i)|10110> + (0.1360-0.1105i)|10111> + (-0.1792-0.1828i)|11000> + (0.0745+0.1021i)|11001> + (-0.0508-0.1508i)|11010> + (0.0675-0.0641i)|11011> + (0.1053+0.0410i)|11100> + (0.1019-0.0258i)|11101> + (0.1671+0.1901i)|11110> + (0.0811-0.0270i)|11111>\n  |11000> -> (0.1268-0.0119i)|00000> + (-0.0972+0.0728i)|00001> + (-0.2800-0.1049i)|00010> + (0.0946-0.0412i)|00011> + (0.2887-0.0940i)|00100> + (0.1368-0.0531i)|00101> + (-0.1941+0.0018i)|00110> + (0.0081+0.0826i)|00111> + (0.1904+0.0715i)|01000> + (0.0753+0.0246i)|01001> + (0.2748+0.0765i)|01010> + (0.1005-0.1587i)|01011> + (-0.2677+0.0388i)|01100> + (0.1535+0.0171i)|01101> + (-0.0968-0.0380i)|01110> + (0.0372-0.1258i)|01111> + (0.1115-0.0111i)|10000> + (-0.0058-0.0798i)|10001> + (0.0280+0.1439i)|10010> + (-0.1411-0.1698i)|10011> + (-0.1360+0.1105i)|10100> + (-0.1794-0.1532i)|10101> + (-0.0421-0.0729i)|10110> + (-0.1327-0.1020i)|10111> + (-0.0675+0.0641i)|11000> + (-0.0508-0.1508i)|11001> + (0.0745+0.1021i)|11010> + (0.1792+0.1828i)|11011> + (-0.0811+0.0270i)|11100> + (0.1671+0.1901i)|11101> + (0.1019-0.0258i)|11110> + (-0.1053-0.0410i)|11111>\n  |11001> -> (-0.1587-0.1005i)|00000> + (0.0765-0.2748i)|00001> + (0.0246-0.0753i)|00010> + (0.0715-0.1904i)|00011> + (-0.1258-0.0372i)|00100> + (-0.0380+0.0968i)|00101> + (0.0171-0.1535i)|00110> + (0.0388+0.2677i)|00111> + (-0.0412-0.0946i)|01000> + (-0.1049+0.2800i)|01001> + (0.0728+0.0972i)|01010> + (-0.0119-0.1268i)|01011> + (0.0826-0.0081i)|01100> + (0.0018+0.1941i)|01101> + (-0.0531-0.1368i)|01110> + (-0.0940-0.2887i)|01111> + (-0.1828+0.1792i)|10000> + (-0.1021+0.0745i)|10001> + (0.1508-0.0508i)|10010> + (-0.0641-0.0675i)|10011> + (0.0410-0.1053i)|10100> + (0.0258+0.1019i)|10101> + (-0.1901+0.1671i)|10110> + (-0.0270-0.0811i)|10111> + (0.1698-0.1411i)|11000> + (-0.1439+0.0280i)|11001> + (0.0798-0.0058i)|11010> + (0.0111+0.1115i)|11011> + (0.1020-0.1327i)|11100> + (0.0729-0.0421i)|11101> + (0.1532-0.1794i)|11110> + (-0.1105-0.1360i)|11111>\n  |11010> -> (-0.1174-0.0822i)|00000> + (0.2737-0.0310i)|00001> + (0.0582+0.1020i)|00010> + (-0.1442-0.0080i)|00011> + (0.0718+0.0864i)|00100> + (0.1676-0.0868i)|00101> + (-0.0817-0.0125i)|00110> + (-0.3161+0.0573i)|00111> + (0.1167+0.1877i)|01000> + (0.2658+0.0281i)|01001> + (0.0310-0.0261i)|01010> + (0.2057+0.0030i)|01011> + (0.1047+0.0910i)|01100> + (-0.0655+0.0283i)|01101> + (0.0837-0.0765i)|01110> + (-0.2893+0.0646i)|01111> + (-0.1541-0.1940i)|10000> + (0.1013+0.0188i)|10001> + (-0.0501-0.0149i)|10010> + (-0.0472+0.1107i)|10011> + (-0.1666-0.0572i)|10100> + (-0.0408+0.0255i)|10101> + (-0.1867-0.0940i)|10110> + (-0.0139-0.2103i)|10111> + (-0.1505-0.2319i)|11000> + (-0.0413-0.0406i)|11001> + (0.1130+0.1030i)|11010> + (-0.0455+0.1013i)|11011> + (0.1058+0.0796i)|11100> + (-0.0155-0.0883i)|11101> + (-0.2150-0.0643i)|11110> + (0.0625+0.1240i)|11111>\n  |11011> -> (-0.0030+0.2057i)|00000> + (0.0261+0.0310i)|00001> + (-0.0281+0.2658i)|00010> + (-0.1877+0.1167i)|00011> + (-0.0646-0.2893i)|00100> + (0.0765+0.0837i)|00101> + (-0.0283-0.0655i)|00110> + (-0.0910+0.1047i)|00111> + (0.0080-0.1442i)|01000> + (-0.1020+0.0582i)|01001> + (0.0310+0.2737i)|01010> + (0.0822-0.1174i)|01011> + (-0.0573-0.3161i)|01100> + (0.0125-0.0817i)|01101> + (0.0868+0.1676i)|01110> + (-0.0864+0.0718i)|01111> + (0.1013+0.0455i)|10000> + (0.1030-0.1130i)|10001> + (-0.0406+0.0413i)|10010> + (-0.2319+0.1505i)|10011> + (0.1240-0.0625i)|10100> + (-0.0643+0.2150i)|10101> + (-0.0883+0.0155i)|10110> + (0.0796-0.1058i)|10111> + (0.1107+0.0472i)|11000> + (-0.0149+0.0501i)|11001> + (0.0188-0.1013i)|11010> + (-0.1940+0.1541i)|11011> + (-0.2103+0.0139i)|11100> + (-0.0940+0.1867i)|11101> + (0.0255+0.0408i)|11110> + (-0.0572+0.1666i)|11111>\n  |11100> -> (-0.1530+0.0102i)|00000> + (-0.0731+0.0034i)|00001> + (0.1983+0.1111i)|00010> + (0.1052-0.1829i)|00011> + (-0.0668-0.1124i)|00100> + (-0.0266-0.3131i)|00101> + (0.1014-0.0311i)|00110> + (-0.1183-0.1523i)|00111> + (0.1851+0.0200i)|01000> + (-0.0141-0.0943i)|01001> + (0.1602+0.0756i)|01010> + (-0.1404+0.2518i)|01011> + (-0.1615-0.1216i)|01100> + (0.0461+0.2406i)|01101> + (-0.1294+0.0932i)|01110> + (-0.0548-0.0415i)|01111> + (-0.0187+0.0786i)|10000> + (0.1312+0.0541i)|10001> + (0.1555-0.1404i)|10010> + (-0.0432+0.1508i)|10011> + (-0.1892+0.1305i)|10100> + (0.1264+0.0992i)|10101> + (0.0063-0.0660i)|10110> + (0.1605+0.0816i)|10111> + (-0.0811+0.1459i)|11000> + (-0.0345-0.0563i)|11001> + (-0.2253+0.1495i)|11010> + (-0.0928+0.0868i)|11011> + (0.1595-0.0872i)|11100> + (0.1308+0.1516i)|11101> + (-0.0502+0.0009i)|11110> + (-0.1073-0.0456i)|11111>\n  |11101> -> (0.2518+0.1404i)|00000> + (0.0756-0.1602i)|00001> + (-0.0943+0.0141i)|00010> + (0.0200-0.1851i)|00011> + (-0.0415+0.0548i)|00100> + (0.0932+0.1294i)|00101> + (0.2406-0.0461i)|00110> + (-0.1216+0.1615i)|00111> + (-0.1829-0.1052i)|01000> + (0.1111-0.1983i)|01001> + (0.0034+0.0731i)|01010> + (0.0102+0.1530i)|01011> + (-0.1523+0.1183i)|01100> + (-0.0311-0.1014i)|01101> + (-0.3131+0.0266i)|01110> + (-0.1124+0.0668i)|01111> + (-0.0868-0.0928i)|10000> + (-0.1495-0.2253i)|10001> + (0.0563-0.0345i)|10010> + (-0.1459-0.0811i)|10011> + (0.0456-0.1073i)|10100> + (-0.0009-0.0502i)|10101> + (-0.1516+0.1308i)|10110> + (0.0872+0.1595i)|10111> + (-0.1508-0.0432i)|11000> + (0.1404+0.1555i)|11001> + (-0.0541+0.1312i)|11010> + (-0.0786-0.0187i)|11011> + (-0.0816+0.1605i)|11100> + (0.0660+0.0063i)|11101> + (-0.0992+0.1264i)|11110> + (-0.1305-0.1892i)|11111>\n  |11110> -> (0.0318+0.1855i)|00000> + (0.2409-0.0897i)|00001> + (-0.0723-0.0161i)|00010> + (-0.1218-0.0567i)|00011> + (-0.0012+0.1751i)|00100> + (0.1116+0.0054i)|00101> + (0.1293+0.3123i)|00110> + (-0.0176+0.0812i)|00111> + (0.0319+0.2602i)|01000> + (-0.1890+0.0689i)|01001> + (0.0936-0.0761i)|01010> + (-0.1854-0.0123i)|01011> + (0.0288-0.0516i)|01100> + (0.1753+0.0352i)|01101> + (0.0792+0.2528i)|01110> + (0.1003-0.1237i)|01111> + (-0.1215-0.0090i)|10000> + (0.1772-0.1620i)|10001> + (-0.0411-0.1388i)|10010> + (-0.0371+0.0194i)|10011> + (-0.1518-0.0592i)|10100> + (0.0775-0.0174i)|10101> + (-0.2011-0.0135i)|10110> + (-0.0499+0.1987i)|10111> + (0.0377-0.0318i)|11000> + (0.1945-0.2122i)|11001> + (-0.0126-0.0948i)|11010> + (0.1487-0.0702i)|11011> + (-0.0744-0.0783i)|11100> + (-0.0724-0.0562i)|11101> + (0.2246+0.0224i)|11110> + (-0.0310+0.1314i)|11111>\n  |11111> -> (0.0123-0.1854i)|00000> + (0.0761+0.0936i)|00001> + (-0.0689-0.1890i)|00010> + (-0.2602+0.0319i)|00011> + (0.1237+0.1003i)|00100> + (-0.2528+0.0792i)|00101> + (-0.0352+0.1753i)|00110> + (0.0516+0.0288i)|00111> + (0.0567-0.1218i)|01000> + (0.0161-0.0723i)|01001> + (0.0897+0.2409i)|01010> + (-0.1855+0.0318i)|01011> + (-0.0812-0.0176i)|01100> + (-0.3123+0.1293i)|01101> + (-0.0054+0.1116i)|01110> + (-0.1751-0.0012i)|01111> + (-0.0702-0.1487i)|10000> + (-0.0948+0.0126i)|10001> + (-0.2122-0.1945i)|10010> + (-0.0318-0.0377i)|10011> + (0.1314+0.0310i)|10100> + (0.0224-0.2246i)|10101> + (-0.0562+0.0724i)|10110> + (-0.0783+0.0744i)|10111> + (0.0194+0.0371i)|11000> + (-0.1388+0.0411i)|11001> + (-0.1620-0.1772i)|11010> + (-0.0090+0.1215i)|11011> + (0.1987+0.0499i)|11100> + (-0.0135+0.2011i)|11101> + (-0.0174-0.0775i)|11110> + (-0.0592+0.1518i)|11111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "The following 5-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\ncx q[1],q[0];\nt q[2];\nt q[2];\ny q[1];\nrz(3.893759820960499) q[3];\ns q[0];\nh q[3];\nz q[4];\nrz(1.4826818544450509) q[3];\nh q[0];\ns q[0];\ns q[3];\ny q[3];\ncz q[2],q[1];\nry(5.19021539939376) q[2];\nz q[3];\ncz q[3],q[0];\ns q[0];\ncz q[1],q[2];\nh q[1];\nry(0.6286555281683881) q[4];\ncz q[1],q[0];\nz q[2];\ny q[2];\nrz(1.2154038069920456) q[3];\nry(2.284661366303957) q[1];\nry(0.7273856311806477) q[0];\nrx(6.103324226420383) q[0];\nry(2.720578195198957) q[3];\nt q[2];\ns q[4];\ns q[0];\nz q[3];\nt q[4];\nrz(4.766567335459742) q[2];\nrz(5.517622113126137) q[0];\ncz q[3],q[2];\nry(2.738697716654763) q[4];\nx q[3];\ns q[1];\nry(0.9646067882777152) q[1];\nx q[4];\ns q[0];\nrx(2.793168155307437) q[4];\nrx(1.9924041166324504) q[0];\nz q[1];\nz q[3];\ncx q[2],q[0];\ns q[2];\nry(0.5910087089385755) q[1];\ns q[2];\ns q[1];\ns q[4];\ncz q[2],q[3];\nx q[3];\nt q[4];\nrx(5.807481689875391) q[1];\nt q[3];\nrz(0.3288284330823977) q[4];\ncx q[1],q[2];\ncz q[2],q[4];\ny q[4];\nx q[3];\nh q[3];\ncz q[0],q[4];\nh q[3];\nz q[2];\nh q[4];\nry(6.177140953420299) q[2];\ny q[1];\nrz(0.4781329541815844) q[2];\ns q[2];\nt q[2];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00000> -> (-0.2106+0.2778i)|00000> + (-0.0131+0.0927i)|00001> + (0.0212+0.1938i)|00010> + (0.0119-0.0364i)|00011> + (0.0178-0.0324i)|00100> + (0.1860-0.0960i)|00101> + (0.0731+0.0478i)|00110> + (-0.2998-0.1326i)|00111> + (0.1982+0.0399i)|01000> + (0.0015-0.1262i)|01001> + (0.0208+0.1325i)|01010> + (0.0867-0.0259i)|01011> + (-0.0211+0.0725i)|01100> + (-0.0998-0.0794i)|01101> + (-0.0135+0.1448i)|01110> + (-0.2086-0.0940i)|01111> + (-0.0678+0.1314i)|10000> + (-0.0523+0.2177i)|10001> + (0.0198+0.0686i)|10010> + (0.0260-0.1116i)|10011> + (0.0796-0.1003i)|10100> + (0.0672-0.0434i)|10101> + (0.1490+0.1276i)|10110> + (-0.1313-0.0348i)|10111> + (0.0901-0.0045i)|11000> + (0.0587-0.3143i)|11001> + (0.0287+0.0399i)|11010> + (0.2060-0.0420i)|11011> + (-0.1064+0.1598i)|11100> + (-0.0472-0.0384i)|11101> + (-0.1034+0.3253i)|11110> + (-0.0829-0.0252i)|11111>\n  |00001> -> (0.0973+0.2121i)|00000> + (0.1184-0.0619i)|00001> + (-0.0814+0.0832i)|00010> + (0.0625+0.0594i)|00011> + (-0.0761+0.0172i)|00100> + (0.0063-0.1458i)|00101> + (-0.1252+0.0546i)|00110> + (-0.0410-0.1936i)|00111> + (-0.1334-0.3003i)|01000> + (-0.0587-0.0585i)|01001> + (-0.1904-0.0788i)|01010> + (0.0278+0.0381i)|01011> + (0.0107+0.0294i)|01100> + (-0.0047+0.1969i)|01101> + (-0.0938+0.0364i)|01110> + (0.2765-0.2103i)|01111> + (0.0641+0.0818i)|10000> + (0.3214-0.1051i)|10001> + (-0.0119+0.0427i)|10010> + (0.1292+0.1513i)|10011> + (-0.2015-0.0175i)|10100> + (0.0040-0.0671i)|10101> + (-0.3164+0.0622i)|10110> + (-0.0246-0.0694i)|10111> + (-0.0769-0.1153i)|11000> + (-0.1250-0.1496i)|11001> + (-0.0729-0.0151i)|11010> + (0.0863+0.1014i)|11011> + (0.0275+0.1077i)|11100> + (0.0067+0.0744i)|11101> + (-0.2201+0.0506i)|11110> + (0.0995-0.1031i)|11111>\n  |00010> -> (0.1869-0.1308i)|00000> + (-0.0733+0.1050i)|00001> + (-0.0739-0.1260i)|00010> + (-0.0194-0.0708i)|00011> + (-0.0560+0.0326i)|00100> + (0.1323-0.0197i)|00101> + (-0.1385-0.0218i)|00110> + (-0.2526+0.0029i)|00111> + (0.2577+0.1912i)|01000> + (-0.0483+0.0849i)|01001> + (0.1181+0.1341i)|01010> + (-0.0576+0.0374i)|01011> + (-0.0335+0.0468i)|01100> + (0.0921+0.1759i)|01101> + (0.0294+0.0975i)|01110> + (0.2937-0.0479i)|01111> + (0.0731-0.0674i)|10000> + (-0.2115+0.2225i)|10001> + (-0.0285-0.0353i)|10010> + (-0.0365-0.1931i)|10011> + (-0.1691+0.0667i)|10100> + (0.0448-0.0065i)|10101> + (-0.3121-0.1038i)|10110> + (-0.1051+0.0131i)|10111> + (0.1257+0.0556i)|11000> + (-0.1575+0.2020i)|11001> + (0.0616+0.0347i)|11010> + (-0.1255+0.0755i)|11011> + (-0.1311+0.0762i)|11100> + (0.0463+0.0740i)|11101> + (0.0109+0.2326i)|11110> + (0.1098-0.0380i)|11111>\n  |00011> -> (0.0453-0.2973i)|00000> + (0.0858-0.0102i)|00001> + (0.0675-0.1772i)|00010> + (0.0690+0.0278i)|00011> + (0.0535-0.0014i)|00100> + (0.1050-0.1543i)|00101> + (0.0704-0.0898i)|00110> + (-0.1914-0.2531i)|00111> + (0.0048-0.2540i)|01000> + (0.0611+0.1214i)|01001> + (-0.1308-0.0142i)|01010> + (-0.0662-0.0134i)|01011> + (0.0042+0.0680i)|01100> + (0.0699-0.1328i)|01101> + (-0.0789+0.1037i)|01110> + (-0.1319+0.1851i)|01111> + (-0.0096-0.1277i)|10000> + (0.2287+0.0081i)|10001> + (0.0019-0.0734i)|10010> + (0.1494+0.0644i)|10011> + (0.1248+0.0545i)|10100> + (0.0401-0.0725i)|10101> + (0.2039-0.1619i)|10110> + (-0.0900-0.0855i)|10111> + (-0.0141-0.1103i)|11000> + (0.1033+0.3111i)|11001> + (-0.0409-0.0004i)|11010> + (-0.1752-0.0542i)|11011> + (-0.0214+0.1924i)|11100> + (0.0253-0.0465i)|11101> + (-0.2231+0.2118i)|11110> + (-0.0466+0.0844i)|11111>\n  |00100> -> (0.1642+0.1236i)|00000> + (0.0516-0.0167i)|00001> + (-0.3255+0.0413i)|00010> + (0.0855-0.0098i)|00011> + (0.0922+0.0430i)|00100> + (0.1683+0.3027i)|00101> + (0.0075-0.0346i)|00110> + (-0.0752+0.1805i)|00111> + (0.0315-0.1143i)|01000> + (-0.0886+0.0076i)|01001> + (-0.2330+0.0273i)|01010> + (0.0605+0.1217i)|01011> + (-0.1213-0.0585i)|01100> + (0.1157-0.1590i)|01101> + (0.0728+0.0153i)|01110> + (-0.0505+0.1345i)|01111> + (0.0706+0.0281i)|10000> + (0.1286+0.0223i)|10001> + (-0.1321+0.0448i)|10010> + (0.1914+0.0289i)|10011> + (0.1817+0.1333i)|10100> + (0.0976+0.1082i)|10101> + (0.0697-0.0850i)|10110> + (-0.0073+0.0779i)|10111> + (0.0116-0.0364i)|11000> + (-0.1953-0.0313i)|11001> + (-0.0985+0.0235i)|11010> + (0.0747+0.3289i)|11011> + (-0.2655-0.1843i)|11100> + (0.0251-0.0726i)|11101> + (0.1923+0.0669i)|11110> + (-0.0030+0.0718i)|11111>\n  |00101> -> (0.1269-0.0493i)|00000> + (-0.0536-0.0772i)|00001> + (-0.1380-0.1495i)|00010> + (-0.0739+0.1047i)|00011> + (-0.0076-0.1433i)|00100> + (0.2274-0.0009i)|00101> + (0.0205+0.0691i)|00110> + (-0.1210+0.0339i)|00111> + (-0.1770+0.0801i)|01000> + (-0.0130+0.0430i)|01001> + (0.1284-0.3238i)|01010> + (-0.0485+0.0845i)|01011> + (-0.0775+0.0435i)|01100> + (-0.3270+0.0011i)|01101> + (0.0240+0.0320i)|01110> + (-0.1299-0.1619i)|01111> + (0.0400-0.0163i)|10000> + (-0.0708-0.1964i)|10001> + (-0.0656-0.0577i)|10010> + (-0.2390+0.2113i)|10011> + (0.0357-0.3402i)|10100> + (0.0864-0.0263i)|10101> + (0.0321+0.1906i)|10110> + (-0.0543+0.0350i)|10111> + (-0.0562+0.0470i)|11000> + (-0.0814+0.0771i)|11001> + (0.0268-0.1462i)|11010> + (-0.1580+0.1564i)|11011> + (-0.1867+0.0580i)|11100> + (-0.1343+0.0306i)|11101> + (0.0295+0.1237i)|11110> + (-0.0704-0.0464i)|11111>\n  |00110> -> (0.0770+0.1050i)|00000> + (-0.0657-0.0284i)|00001> + (-0.2139+0.1360i)|00010> + (-0.1247+0.0606i)|00011> + (0.0750+0.1082i)|00100> + (-0.0468-0.2212i)|00101> + (0.0015-0.0704i)|00110> + (-0.0091-0.1473i)|00111> + (-0.1192+0.1496i)|01000> + (-0.0744-0.0249i)|01001> + (0.2317-0.1932i)|01010> + (0.0664+0.0592i)|01011> + (0.0642+0.0910i)|01100> + (0.2767-0.1533i)|01101> + (-0.0477-0.0006i)|01110> + (0.0352+0.1820i)|01111> + (0.0391+0.0224i)|10000> + (-0.1348-0.1220i)|10001> + (-0.0809+0.0784i)|10010> + (-0.3186+0.0722i)|10011> + (0.1195+0.2828i)|10100> + (-0.0435-0.0893i)|10101> + (0.0595-0.1834i)|10110> + (-0.0285-0.0521i)|10111> + (-0.0374+0.0580i)|11000> + (-0.1317-0.0922i)|11001> + (0.0837-0.0938i)|11010> + (0.1233+0.1916i)|11011> + (0.1229+0.2309i)|11100> + (0.0926-0.0864i)|11101> + (-0.1383-0.0017i)|11110> + (0.0360+0.0776i)|11111>\n  |00111> -> (0.1772+0.0334i)|00000> + (0.0199+0.0691i)|00001> + (-0.2979-0.1218i)|00010> + (0.0099-0.1004i)|00011> + (0.0331-0.0932i)|00100> + (-0.2484-0.1625i)|00101> + (0.0315+0.0411i)|00110> + (0.1530-0.1241i)|00111> + (0.1450+0.0009i)|01000> + (-0.0605+0.0495i)|01001> + (-0.0143+0.2269i)|01010> + (-0.0057+0.1301i)|01011> + (0.1404-0.0155i)|01100> + (-0.2290-0.1031i)|01101> + (-0.0593-0.0321i)|01110> + (-0.1106-0.0714i)|01111> + (0.0662+0.0064i)|10000> + (0.0019+0.1448i)|10001> + (-0.1312-0.0321i)|10010> + (0.0925-0.2375i)|10011> + (0.1034-0.2100i)|10100> + (-0.1113-0.0394i)|10101> + (0.0891+0.1252i)|10110> + (0.0534-0.0734i)|10111> + (0.0453-0.0179i)|11000> + (-0.1829+0.0668i)|11001> + (0.0153+0.1000i)|11010> + (-0.0808+0.2952i)|11011> + (0.3271+0.0295i)|11100> + (-0.1077-0.0185i)|11101> + (-0.1260-0.1296i)|11110> + (-0.0507-0.0062i)|11111>\n  |01000> -> (-0.3272+0.1353i)|00000> + (-0.0150+0.0525i)|00001> + (-0.1606+0.1527i)|00010> + (0.0424+0.0182i)|00011> + (0.0021-0.0181i)|00100> + (0.2149+0.0101i)|00101> + (-0.0404+0.0739i)|00110> + (-0.0816-0.3618i)|00111> + (-0.1894-0.0339i)|01000> + (-0.0838+0.1212i)|01001> + (0.0800-0.0224i)|01010> + (-0.0696-0.0519i)|01011> + (0.0661-0.0486i)|01100> + (0.0916+0.0734i)|01101> + (0.1298-0.0695i)|01110> + (-0.0438+0.1426i)|01111> + (-0.1240+0.0821i)|10000> + (-0.0414+0.1322i)|10001> + (-0.0454+0.0703i)|10010> + (0.1068+0.0254i)|10011> + (0.0489-0.0585i)|10100> + (0.0869-0.0068i)|10101> + (-0.1145+0.1401i)|10110> + (-0.0566-0.1392i)|10111> + (-0.0888+0.0014i)|11000> + (-0.2535+0.2625i)|11001> + (0.0148-0.0167i)|11010> + (-0.1544-0.1464i)|11011> + (0.2017-0.0822i)|11100> + (0.0343+0.0364i)|11101> + (0.3343-0.1022i)|11110> + (-0.0146+0.0561i)|11111>\n  |01001> -> (0.0534+0.1435i)|00000> + (0.1406+0.0078i)|00001> + (-0.0765-0.0741i)|00010> + (-0.0106+0.0904i)|00011> + (-0.0733-0.0312i)|00100> + (0.0146-0.0925i)|00101> + (-0.1336-0.0795i)|00110> + (0.1830-0.0444i)|00111> + (-0.0557+0.3686i)|01000> + (0.0502+0.0487i)|01001> + (0.0456+0.2064i)|01010> + (0.0316-0.0193i)|01011> + (-0.0196-0.0182i)|01100> + (0.1265-0.1879i)|01101> + (0.0348+0.0583i)|01110> + (-0.3348-0.1108i)|01111> + (0.0378+0.0615i)|10000> + (0.3392+0.0773i)|10001> + (-0.0294-0.0090i)|10010> + (-0.0485+0.2180i)|10011> + (-0.1670-0.1246i)|10100> + (0.0142-0.0385i)|10101> + (-0.2733-0.2451i)|10110> + (0.0703-0.0224i)|10111> + (0.0067+0.1573i)|11000> + (0.1198+0.1303i)|11001> + (0.0349+0.0731i)|11010> + (0.0605-0.0614i)|11011> + (-0.0337-0.0934i)|11100> + (0.0426-0.0812i)|11101> + (0.0499+0.1332i)|11110> + (-0.1416-0.0214i)|11111>\n  |01010> -> (0.1315+0.1372i)|00000> + (-0.1497+0.0057i)|00001> + (-0.0238-0.0800i)|00010> + (0.0151-0.0823i)|00011> + (-0.0772-0.0262i)|00100> + (0.0298+0.1094i)|00101> + (-0.1181-0.0875i)|00110> + (-0.1466-0.0362i)|00111> + (0.0221-0.3440i)|01000> + (0.0566+0.0174i)|01001> + (-0.0270-0.2135i)|01010> + (0.0528-0.0177i)|01011> + (0.0291+0.0038i)|01100> + (0.1021-0.1845i)|01101> + (-0.0157-0.0903i)|01110> + (-0.3287-0.1466i)|01111> + (0.0697+0.0527i)|10000> + (-0.3643-0.0451i)|10001> + (-0.0103-0.0157i)|10010> + (0.0636-0.2017i)|10011> + (-0.1872-0.1135i)|10100> + (0.0043+0.0435i)|10101> + (-0.2381-0.2562i)|10110> + (-0.0612-0.0124i)|10111> + (-0.0202-0.1439i)|11000> + (0.1475+0.0573i)|11001> + (-0.0315-0.0756i)|11010> + (0.1132-0.0505i)|11011> + (0.0667+0.0605i)|11100> + (0.0335-0.0814i)|11101> + (0.0089-0.2000i)|11110> + (-0.1396-0.0363i)|11111>\n  |01011> -> (0.3194-0.1714i)|00000> + (0.0148+0.0733i)|00001> + (0.1595-0.1296i)|00010> + (0.0332+0.0343i)|00011> + (0.0088+0.0351i)|00100> + (0.2213-0.0106i)|00101> + (0.0595-0.0468i)|00110> + (-0.0471-0.3394i)|00111> + (-0.1471+0.0443i)|01000> + (0.0699-0.1244i)|01001> + (0.1035+0.0177i)|01010> + (0.0643+0.0607i)|01011> + (0.0614-0.0493i)|01100> + (-0.0886-0.0195i)|01101> + (0.1448-0.0576i)|01110> + (0.1217-0.1419i)|01111> + (0.1181-0.0984i)|10000> + (0.0217+0.1944i)|10001> + (0.0467-0.0644i)|10010> + (0.0792+0.0638i)|10011> + (-0.0297+0.1080i)|10100> + (0.0912-0.0136i)|10101> + (0.1474-0.0690i)|10110> + (-0.0418-0.1310i)|10111> + (-0.0651+0.0303i)|11000> + (0.2186-0.2716i)|11001> + (0.0268-0.0042i)|11010> + (0.1448+0.1696i)|11011> + (0.1860-0.0943i)|11100> + (-0.0305-0.0150i)|11101> + (0.3618-0.0709i)|11110> + (0.0458-0.0609i)|11111>\n  |01100> -> (0.0795+0.1961i)|00000> + (0.0405-0.0150i)|00001> + (-0.2570-0.2702i)|00010> + (0.0142+0.0732i)|00011> + (0.0569+0.0358i)|00100> + (-0.0101+0.3518i)|00101> + (0.0213+0.0116i)|00110> + (-0.2183+0.0546i)|00111> + (-0.0235+0.1048i)|01000> + (0.0846+0.0427i)|01001> + (0.0399+0.1483i)|01010> + (0.0704-0.1241i)|01011> + (0.0826+0.1309i)|01100> + (-0.1034+0.1552i)|01101> + (-0.0364-0.0698i)|01110> + (0.0892+0.0166i)|01111> + (0.0445+0.0670i)|10000> + (0.0820+0.0148i)|10001> + (-0.1269-0.0924i)|10010> + (-0.0238+0.1735i)|10011> + (0.1096+0.0912i)|10100> + (0.0276+0.1423i)|10101> + (0.0747+0.0663i)|10110> + (-0.0828+0.0471i)|10111> + (-0.0012+0.0276i)|11000> + (0.1634+0.1500i)|11001> + (0.0269+0.0659i)|11010> + (0.2338-0.2566i)|11011> + (0.1380+0.3404i)|11100> + (-0.0206+0.0756i)|11101> + (-0.0591-0.2002i)|11110> + (0.0448-0.0140i)|11111>\n  |01101> -> (0.0802-0.0250i)|00000> + (-0.0053-0.0896i)|00001> + (0.1352-0.1376i)|00010> + (-0.1496+0.0050i)|00011> + (0.0655-0.1313i)|00100> + (0.1472+0.0077i)|00101> + (-0.0422+0.0691i)|00110> + (-0.0374-0.1081i)|00111> + (0.2191+0.0351i)|01000> + (0.0125-0.0513i)|01001> + (-0.3458+0.0766i)|01010> + (0.0562+0.0177i)|01011> + (0.0737-0.0391i)|01100> + (0.3114+0.1997i)|01101> + (0.0133-0.0083i)|01110> + (-0.0634+0.2044i)|01111> + (0.0169-0.0083i)|10000> + (0.0427-0.2072i)|10001> + (0.0524-0.0704i)|10010> + (-0.3571-0.0707i)|10011> + (0.2097-0.2800i)|10100> + (0.0596-0.0181i)|10101> + (-0.1476+0.1608i)|10110> + (-0.0400-0.0400i)|10111> + (0.0829-0.0035i)|11000> + (0.0708-0.0799i)|11001> + (-0.1366+0.0580i)|11010> + (0.1081+0.0838i)|11011> + (0.1705-0.0617i)|11100> + (0.1435+0.0515i)|11101> + (0.0732-0.0234i)|11110> + (-0.0037+0.0899i)|11111>\n  |01110> -> (-0.0768+0.0713i)|00000> + (-0.0169-0.0907i)|00001> + (-0.1453+0.0493i)|00010> + (-0.1442-0.0094i)|00011> + (-0.0538+0.1463i)|00100> + (0.1731-0.0656i)|00101> + (0.0445-0.0655i)|00110> + (0.0119-0.0870i)|00111> + (0.2056+0.0164i)|01000> + (0.0068+0.0523i)|01001> + (-0.3604+0.0427i)|01010> + (-0.0575-0.0544i)|01011> + (0.0461-0.0575i)|01100> + (-0.3021-0.1601i)|01101> + (0.0311+0.0013i)|01110> + (0.0843-0.2033i)|01111> + (-0.0121+0.0248i)|10000> + (0.0221-0.2204i)|10001> + (-0.0633+0.0347i)|10010> + (-0.3339-0.0976i)|10011> + (-0.1893+0.3163i)|10100> + (0.0632-0.0500i)|10101> + (0.1528-0.1416i)|10110> + (-0.0177-0.0368i)|10111> + (0.0774-0.0068i)|11000> + (-0.0265+0.0955i)|11001> + (-0.1462+0.0434i)|11010> + (-0.0918-0.1708i)|11011> + (0.1147-0.1167i)|11100> + (-0.1345-0.0360i)|11101> + (0.1129+0.0117i)|11110> + (0.0121-0.0951i)|11111>\n  |01111> -> (0.0989+0.1920i)|00000> + (-0.0509+0.0344i)|00001> + (-0.2154-0.2697i)|00010> + (0.0160-0.0613i)|00011> + (0.0884+0.0157i)|00100> + (-0.0252-0.3581i)|00101> + (0.0077+0.0224i)|00110> + (0.2070-0.0334i)|00111> + (-0.0233-0.0798i)|01000> + (0.0803+0.0327i)|01001> + (0.0277-0.1880i)|01010> + (0.0876-0.1243i)|01011> + (-0.0910-0.1157i)|01100> + (-0.0153+0.1485i)|01101> + (0.0329+0.0748i)|01110> + (0.0900+0.0638i)|01111> + (0.0480+0.0638i)|10000> + (-0.1188+0.0239i)|10001> + (-0.1081-0.0956i)|10010> + (0.0881-0.1296i)|10011> + (0.1923+0.0586i)|10100> + (-0.0435-0.1399i)|10101> + (0.0325+0.0857i)|10110> + (0.0832-0.0364i)|10111> + (-0.0142-0.0146i)|11000> + (0.1663+0.1287i)|11001> + (-0.0019-0.0875i)|11010> + (0.2725-0.2446i)|11011> + (-0.1602-0.3108i)|11100> + (0.0142+0.0649i)|11101> + (0.0413+0.2149i)|11110> + (0.0507+0.0050i)|11111>\n  |10000> -> (-0.1377-0.0042i)|00000> + (0.0590-0.1123i)|00001> + (-0.0968+0.0367i)|00010> + (-0.1112-0.0326i)|00011> + (-0.0691+0.0470i)|00100> + (0.0791+0.0305i)|00101> + (0.1421-0.1159i)|00110> + (0.0202-0.1517i)|00111> + (-0.0619-0.0360i)|01000> + (0.2678-0.2556i)|01001> + (0.0521-0.0009i)|01010> + (0.1485+0.1453i)|01011> + (-0.2167+0.0725i)|01100> + (0.0415+0.0211i)|01101> + (-0.3292+0.0838i)|01110> + (-0.0158+0.0548i)|01111> + (0.3388-0.0598i)|10000> + (-0.0242+0.0448i)|10001> + (0.1981-0.1211i)|10010> + (0.0456+0.0054i)|10011> + (0.0447-0.0216i)|10100> + (-0.2048-0.0494i)|10101> + (-0.0602+0.0270i)|10110> + (0.0110+0.3759i)|10111> + (0.1889+0.0498i)|11000> + (-0.1245+0.0858i)|11001> + (-0.0877+0.0188i)|11010> + (-0.0512-0.0648i)|11011> + (0.1017-0.0131i)|11100> + (-0.0999-0.0704i)|11101> + (0.1359-0.0054i)|11110> + (0.0344-0.1340i)|11111>\n  |10001> -> (-0.0098+0.0455i)|00000> + (-0.3112-0.1424i)|00001> + (-0.0261-0.0643i)|00010> + (0.0850-0.2080i)|00011> + (0.1365+0.1601i)|00100> + (-0.0010-0.0318i)|00101> + (0.2162+0.2960i)|00110> + (0.0825-0.0018i)|00111> + (-0.0599+0.1354i)|01000> + (-0.1263-0.1416i)|01001> + (-0.0016+0.0927i)|01010> + (-0.0446+0.0640i)|01011> + (0.0308+0.1183i)|01100> + (0.0602-0.0687i)|01101> + (-0.0400-0.1143i)|01110> + (-0.1220-0.0706i)|01111> + (-0.0123-0.1315i)|10000> + (0.1157+0.0787i)|10001> + (0.0702+0.1082i)|10010> + (-0.0417+0.0783i)|10011> + (-0.0450-0.0806i)|10100> + (-0.0196+0.0810i)|10101> + (-0.0588-0.1330i)|10110> + (-0.2011+0.0190i)|10111> + (0.0766-0.3649i)|11000> + (0.0473+0.0602i)|11001> + (-0.0359-0.2098i)|11010> + (0.0101-0.0308i)|11011> + (-0.0059-0.0666i)|11100> + (-0.1317+0.1872i)|11101> + (0.0020+0.0411i)|11110> + (0.3246+0.1199i)|11111>\n  |10010> -> (0.0223+0.0654i)|00000> + (0.3530+0.1135i)|00001> + (0.0009-0.0519i)|00010> + (-0.0979+0.1841i)|00011> + (0.1688+0.1557i)|00100> + (0.0164+0.0493i)|00101> + (0.1739+0.2908i)|00110> + (-0.0465-0.0249i)|00111> + (0.0445-0.1269i)|01000> + (-0.1443-0.0474i)|01001> + (0.0166-0.1001i)|01010> + (-0.1115+0.0583i)|01011> + (-0.0654-0.0699i)|01100> + (0.0483-0.0624i)|01101> + (-0.0243+0.2027i)|01110> + (-0.1224-0.0877i)|01111> + (-0.1020-0.1635i)|10000> + (-0.1334-0.0682i)|10001> + (0.0045+0.0919i)|10010> + (0.0492-0.0703i)|10011> + (-0.0626-0.0812i)|10100> + (-0.0233-0.1208i)|10101> + (-0.0452-0.1271i)|10110> + (0.1248+0.0604i)|10111> + (-0.0398+0.3321i)|11000> + (0.0606+0.0239i)|11001> + (0.0110+0.2250i)|11010> + (0.0369-0.0252i)|11011> + (0.0247+0.0479i)|11100> + (-0.1022+0.1761i)|11101> + (0.0301-0.0705i)|11110> + (0.3271+0.1639i)|11111>\n  |10011> -> (0.1437-0.0090i)|00000> + (0.0111-0.2111i)|00001> + (0.0885-0.0212i)|00010> + (-0.0615-0.0638i)|00011> + (0.0677-0.1148i)|00100> + (0.0832+0.0188i)|00101> + (-0.1434+0.0206i)|00110> + (0.0316-0.1356i)|00111> + (-0.0457+0.0046i)|01000> + (-0.2233+0.2569i)|01001> + (0.0647+0.0225i)|01010> + (-0.1434-0.1758i)|01011> + (-0.1914+0.0868i)|01100> + (-0.0401+0.0057i)|01101> + (-0.3647+0.0497i)|01110> + (0.0550-0.0550i)|01111> + (-0.3472+0.1016i)|10000> + (-0.0119+0.0875i)|10001> + (-0.1859+0.0907i)|10010> + (0.0241+0.0161i)|10011> + (-0.0491+0.0509i)|10100> + (-0.2194-0.0258i)|10101> + (0.0532+0.0100i)|10110> + (-0.0212+0.3369i)|10111> + (0.1284-0.0413i)|11000> + (0.1065-0.0868i)|11001> + (-0.1252-0.0272i)|11010> + (0.0510+0.0770i)|11011> + (0.0886-0.0236i)|11100> + (0.0881+0.0045i)|11101> + (0.1451+0.0099i)|11110> + (-0.1292+0.1498i)|11111>\n  |10100> -> (0.0003+0.0924i)|00000> + (-0.0613-0.0434i)|00001> + (-0.0520-0.1382i)|00010> + (0.0698-0.1744i)|00011> + (-0.0725-0.0973i)|00100> + (-0.0648+0.1269i)|00101> + (-0.0774-0.0952i)|00110> + (-0.0916-0.0260i)|00111> + (-0.0212+0.0645i)|01000> + (-0.1500-0.1651i)|01001> + (0.0038+0.0448i)|01010> + (-0.2435+0.2395i)|01011> + (-0.1205-0.3465i)|01100> + (-0.0733+0.0468i)|01101> + (0.0524+0.2041i)|01110> + (0.0218+0.0316i)|01111> + (-0.0368-0.2098i)|10000> + (0.0140+0.0361i)|10001> + (0.1974+0.3165i)|10010> + (-0.0519+0.0624i)|10011> + (0.0164+0.0368i)|10100> + (0.0869-0.3343i)|10101> + (0.0372+0.0544i)|10110> + (0.2273-0.0013i)|10111> + (0.0321-0.1257i)|11000> + (0.0400+0.0837i)|11001> + (-0.0351-0.1279i)|11010> + (0.1201-0.0751i)|11011> + (0.0203+0.1433i)|11100> + (0.1295-0.1526i)|11101> + (-0.0085-0.0911i)|11110> + (-0.0752-0.0288i)|11111>\n  |10101> -> (0.0505-0.0038i)|00000> + (-0.0893+0.1863i)|00001> + (0.0639-0.0288i)|00010> + (0.3379+0.1486i)|00011> + (-0.2566+0.2230i)|00100> + (0.0471+0.0388i)|00101> + (0.1846-0.1354i)|00110> + (0.0256-0.0475i)|00111> + (0.0960+0.0368i)|01000> + (-0.0909+0.0667i)|01001> + (-0.1375-0.0031i)|01010> + (-0.0924-0.0843i)|01011> + (-0.1761+0.0523i)|01100> + (0.1010+0.1181i)|01101> + (-0.0794+0.0273i)|01110> + (-0.0514+0.0707i)|01111> + (-0.0899+0.0096i)|10000> + (0.0559-0.0645i)|10001> + (-0.1600+0.1130i)|10010> + (-0.1231-0.0919i)|10011> + (0.1174-0.0675i)|10100> + (-0.1279-0.0481i)|10101> + (-0.0898+0.0473i)|10110> + (0.0010+0.1191i)|10111> + (-0.2275-0.0478i)|11000> + (0.0528-0.0068i)|11001> + (0.3388-0.0601i)|11010> + (0.0252+0.0490i)|11011> + (0.0648-0.0053i)|11100> + (-0.3014-0.2232i)|11101> + (0.0473-0.0129i)|11110> + (0.0760-0.1954i)|11111>\n  |10110> -> (-0.0631+0.0270i)|00000> + (-0.0745+0.2126i)|00001> + (-0.0456-0.0107i)|00010> + (0.2971+0.1648i)|00011> + (0.2484-0.2716i)|00100> + (0.0806+0.0173i)|00101> + (-0.1810+0.1064i)|00110> + (0.0394-0.0235i)|00111> + (0.0867+0.0219i)|01000> + (0.0339-0.0791i)|01001> + (-0.1417-0.0171i)|01010> + (0.0811+0.1934i)|01011> + (-0.0985+0.1076i)|01100> + (-0.1020-0.0972i)|01101> + (-0.1340-0.0129i)|01110> + (0.0634-0.0631i)|01111> + (0.1099-0.0656i)|10000> + (0.0556-0.0786i)|10001> + (0.1343-0.0067i)|10010> + (-0.1038-0.0926i)|10011> + (-0.1181+0.0851i)|10100> + (-0.1949+0.0205i)|10101> + (0.0868-0.0310i)|10110> + (-0.0461+0.0721i)|10111> + (-0.2063-0.0229i)|11000> + (-0.0307+0.0185i)|11001> + (0.3615-0.0240i)|11010> + (-0.0108-0.0917i)|11011> + (0.0392-0.0330i)|11100> + (0.2879+0.1751i)|11101> + (0.0676+0.0088i)|11110> + (-0.1029+0.1936i)|11111>\n  |10111> -> (0.0160+0.0983i)|00000> + (0.1220+0.0154i)|00001> + (-0.0375-0.1280i)|00010> + (-0.1188+0.0922i)|00011> + (-0.1818-0.0949i)|00100> + (0.0552-0.1426i)|00101> + (-0.0180-0.0956i)|00110> + (0.0766+0.0283i)|00111> + (-0.0057-0.0524i)|01000> + (-0.1538-0.1392i)|01001> + (0.0293-0.0627i)|01010> + (-0.2922+0.2266i)|01011> + (0.1400+0.3084i)|01100> + (-0.0280+0.0496i)|01101> + (-0.0297-0.2277i)|01110> + (0.0183+0.0557i)|01111> + (-0.0652-0.2164i)|10000> + (-0.0419-0.0311i)|10001> + (0.1515+0.2987i)|10010> + (0.0638-0.0249i)|10011> + (0.0593+0.0447i)|10100> + (-0.0526+0.3611i)|10101> + (0.0110+0.0498i)|10110> + (-0.2019-0.0160i)|10111> + (0.0243+0.0882i)|11000> + (0.0486+0.0740i)|11001> + (-0.0382+0.1888i)|11010> + (0.1384-0.0634i)|11011> + (-0.0294-0.1320i)|11100> + (0.0211-0.1354i)|11101> + (-0.0045+0.1026i)|11110> + (-0.0833-0.0863i)|11111>\n  |11000> -> (0.0753+0.1144i)|00000> + (-0.2174-0.0679i)|00001> + (0.0863+0.0147i)|00010> + (0.1111+0.0284i)|00011> + (0.1079+0.0992i)|00100> + (-0.0257-0.0869i)|00101> + (-0.1283+0.1220i)|00110> + (-0.0855+0.0942i)|00111> + (0.0375-0.0627i)|01000> + (0.3152+0.0433i)|01001> + (0.0743+0.0156i)|01010> + (0.0543+0.2012i)|01011> + (-0.1620-0.1070i)|01100> + (-0.0182+0.0286i)|01101> + (-0.3282-0.1001i)|01110> + (-0.0509+0.0889i)|01111> + (-0.2453-0.2492i)|10000> + (0.0808+0.0349i)|10001> + (-0.1986-0.0072i)|10010> + (-0.0528-0.0102i)|10011> + (-0.0500-0.0548i)|10100> + (0.0783+0.2024i)|10101> + (0.0529-0.0359i)|10110> + (0.1718-0.2696i)|10111> + (-0.0427+0.1799i)|11000> + (-0.1272-0.0391i)|11001> + (-0.1494+0.0100i)|11010> + (-0.0124-0.0766i)|11011> + (0.0580+0.0641i)|11100> + (0.0616-0.0918i)|11101> + (0.1181+0.0693i)|11110> + (0.0969-0.2213i)|11111>\n  |11001> -> (0.0910-0.0016i)|00000> + (0.0625+0.3424i)|00001> + (0.0152+0.0585i)|00010> + (-0.1596+0.1030i)|00011> + (0.0567-0.2060i)|00100> + (-0.0480-0.0019i)|00101> + (-0.0056-0.3142i)|00110> + (-0.0833+0.0005i)|00111> + (-0.1210+0.0341i)|01000> + (0.1332-0.1192i)|01001> + (-0.0474+0.0867i)|01010> + (-0.1015+0.1010i)|01011> + (-0.1112+0.0345i)|01100> + (0.0839+0.0047i)|01101> + (-0.0477-0.2191i)|01110> + (-0.0710-0.1213i)|01111> + (-0.2239+0.0690i)|10000> + (-0.0041-0.1447i)|10001> + (-0.0645-0.0983i)|10010> + (0.0639-0.0298i)|10011> + (-0.0474+0.0851i)|10100> + (0.1419+0.0095i)|10101> + (-0.0270+0.1240i)|10110> + (0.1904-0.0215i)|10111> + (0.2854-0.1419i)|11000> + (-0.0544+0.0391i)|11001> + (0.0767-0.2055i)|11010> + (0.0419-0.0468i)|11011> + (0.0570-0.0158i)|11100> + (-0.1976+0.0093i)|11101> + (0.0016+0.0822i)|11110> + (0.2235+0.2718i)|11111>\n  |11010> -> (-0.0265-0.0740i)|00000> + (-0.1819-0.2362i)|00001> + (-0.0740+0.0286i)|00010> + (0.2054-0.0169i)|00011> + (-0.0431-0.1814i)|00100> + (-0.0063-0.0620i)|00101> + (0.1486-0.2951i)|00110> + (-0.0187+0.0968i)|00111> + (0.0988-0.0832i)|01000> + (-0.2123-0.1631i)|01001> + (0.0738-0.0352i)|01010> + (-0.0732-0.1072i)|01011> + (-0.0711-0.1487i)|01100> + (0.0637-0.0314i)|01101> + (-0.2176+0.0036i)|01110> + (-0.0076-0.1252i)|01111> + (0.1023+0.1843i)|10000> + (0.0553+0.1035i)|10001> + (0.1460-0.0715i)|10010> + (-0.0874+0.0014i)|10011> + (0.0103+0.0824i)|10100> + (0.0135+0.1343i)|10101> + (-0.0784+0.1016i)|10110> + (0.0170-0.2539i)|10111> + (-0.1897+0.2619i)|11000> + (0.0809+0.0797i)|11001> + (-0.1360+0.1193i)|11010> + (0.0212+0.0356i)|11011> + (0.0133+0.0796i)|11100> + (-0.1668+0.1027i)|11101> + (0.0842+0.0231i)|11110> + (0.0640+0.2903i)|11111>\n  |11011> -> (-0.0989-0.0650i)|00000> + (-0.0311+0.2215i)|00001> + (-0.0639-0.0678i)|00010> + (-0.0687+0.1418i)|00011> + (-0.0787+0.1113i)|00100> + (-0.0409-0.0481i)|00101> + (0.1337+0.2240i)|00110> + (-0.1289+0.0490i)|00111> + (-0.0919-0.0198i)|01000> + (-0.3107+0.1184i)|01001> + (-0.0068+0.0652i)|01010> + (0.0400-0.1814i)|01011> + (-0.2078-0.0137i)|01100> + (-0.0645-0.0278i)|01101> + (-0.2158-0.2047i)|01110> + (0.0599+0.0534i)|01111> + (0.2762+0.0969i)|10000> + (0.0256-0.0932i)|10001> + (0.1710+0.1070i)|10010> + (0.0247-0.0476i)|10011> + (0.0536-0.0392i)|10100> + (0.1308+0.1179i)|10101> + (-0.0272-0.0992i)|10110> + (0.2872-0.1606i)|10111> + (0.2517+0.0063i)|11000> + (0.1288-0.0274i)|11001> + (0.0083-0.1357i)|11010> + (-0.0241+0.0769i)|11011> + (0.0932+0.0180i)|11100> + (0.1459+0.0655i)|11101> + (0.0687+0.0937i)|11110> + (-0.1755-0.1186i)|11111>\n  |11100> -> (0.0840-0.0540i)|00000> + (-0.0517+0.1306i)|00001> + (-0.0333+0.1223i)|00010> + (-0.0541+0.1689i)|00011> + (-0.1522+0.1640i)|00100> + (0.1425-0.0149i)|00101> + (0.0749+0.0876i)|00110> + (0.0575+0.0651i)|00111> + (-0.0557-0.0080i)|01000> + (0.0287-0.1867i)|01001> + (-0.0023+0.0880i)|01010> + (-0.3378+0.0799i)|01011> + (0.1667-0.2673i)|01100> + (-0.0533-0.0672i)|01101> + (-0.0594+0.2065i)|01110> + (0.0326+0.0441i)|01111> + (-0.1581+0.1514i)|10000> + (0.0468-0.0502i)|10001> + (0.0140-0.3180i)|10010> + (0.0412-0.0572i)|10011> + (0.0703-0.0450i)|10100> + (-0.3305+0.1178i)|10101> + (-0.0280-0.0547i)|10110> + (-0.1630-0.1098i)|10111> + (0.1177+0.0214i)|11000> + (-0.0317+0.0662i)|11001> + (-0.0285-0.2337i)|11010> + (0.1472-0.0013i)|11011> + (-0.0831+0.0933i)|11100> + (0.1505+0.1168i)|11101> + (0.0352-0.0877i)|11110> + (-0.1249-0.0625i)|11111>\n  |11101> -> (-0.0223-0.0687i)|00000> + (0.2042-0.0322i)|00001> + (-0.0599+0.0355i)|00010> + (-0.1657-0.2709i)|00011> + (0.3338+0.0826i)|00100> + (0.0397-0.0981i)|00101> + (-0.1952+0.0072i)|00110> + (-0.0171+0.0357i)|00111> + (0.0205+0.0867i)|01000> + (-0.0682-0.0895i)|01001> + (-0.1154-0.0751i)|01010> + (-0.1491-0.1699i)|01011> + (-0.0483-0.1695i)|01100> + (-0.0261+0.1265i)|01101> + (-0.1435+0.0265i)|01110> + (-0.0881+0.0348i)|01111> + (0.0495+0.1432i)|10000> + (-0.0809-0.0133i)|10001> + (0.1479-0.1132i)|10010> + (0.0444+0.1270i)|10011> + (-0.1234-0.0546i)|10100> + (-0.0319+0.2380i)|10101> + (0.0835+0.0054i)|10110> + (-0.0072-0.1084i)|10111> + (-0.0852-0.1788i)|11000> + (0.0174+0.0555i)|11001> + (0.3271+0.1229i)|11010> + (0.0377+0.0842i)|11011> + (-0.0006+0.0661i)|11100> + (-0.0088-0.3188i)|11101> + (0.0756+0.0004i)|11110> + (0.1705-0.1315i)|11111>\n  |11110> -> (0.0667-0.0143i)|00000> + (0.1494-0.1080i)|00001> + (0.0187+0.0937i)|00010> + (-0.0174-0.3308i)|00011> + (-0.2896+0.0649i)|00100> + (-0.0812-0.0188i)|00101> + (0.1835+0.0968i)|00110> + (-0.0676-0.0340i)|00111> + (0.0695+0.0567i)|01000> + (0.0994-0.1195i)|01001> + (-0.0650-0.0960i)|01010> + (-0.1901+0.1162i)|01011> + (-0.2305+0.1246i)|01100> + (-0.0405-0.1343i)|01101> + (-0.0088-0.1381i)|01110> + (0.0658+0.0076i)|01111> + (-0.1207+0.0598i)|10000> + (-0.0781+0.0300i)|10001> + (-0.1084-0.2266i)|10010> + (-0.0259+0.1321i)|10011> + (0.1178+0.0014i)|10100> + (0.2102-0.0121i)|10101> + (-0.0746-0.0612i)|10110> + (0.1562+0.0201i)|10111> + (-0.1672-0.1156i)|11000> + (-0.0537+0.0261i)|11001> + (0.2011+0.2140i)|11010> + (0.0936-0.0315i)|11011> + (0.0938-0.0339i)|11100> + (0.1620+0.2852i)|11101> + (0.0046+0.0618i)|11110> + (-0.1714+0.0348i)|11111>\n  |11111> -> (0.0293-0.0725i)|00000> + (-0.1264-0.0216i)|00001> + (-0.0808+0.0975i)|00010> + (0.2332+0.1290i)|00011> + (0.1861+0.1152i)|00100> + (-0.1051+0.0714i)|00101> + (-0.1402+0.0902i)|00110> + (-0.0109-0.0749i)|00111> + (0.0210-0.0784i)|01000> + (-0.0658-0.1933i)|01001> + (0.0757+0.0282i)|01010> + (-0.2888-0.0704i)|01011> + (-0.0235+0.3291i)|01100> + (-0.0702+0.0746i)|01101> + (0.1308-0.1315i)|01110> + (-0.0542+0.0380i)|01111> + (-0.0558+0.1737i)|10000> + (0.0380+0.0260i)|10001> + (0.1629-0.2805i)|10010> + (-0.0858-0.0789i)|10011> + (-0.0652-0.0530i)|10100> + (0.2046-0.2146i)|10101> + (0.0657-0.0396i)|10110> + (0.0904+0.1718i)|10111> + (-0.0092+0.1615i)|11000> + (0.0038+0.0917i)|11001> + (-0.2092-0.0180i)|11010> + (0.1061+0.0551i)|11011> + (0.0379-0.1238i)|11100> + (0.1150-0.2253i)|11101> + (-0.0721+0.0453i)|11110> + (0.0810-0.1057i)|11111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "The following 5-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\nrz(2.37800268252761) q[3];\nrx(2.8923780641064187) q[4];\ny q[3];\ns q[2];\nrz(4.302399126381679) q[3];\nrz(4.1424760047965155) q[4];\nt q[1];\nt q[1];\ncx q[4],q[1];\nz q[0];\nz q[3];\nx q[0];\nry(0.4706815419919275) q[3];\ncx q[1],q[4];\ncz q[3],q[2];\ncz q[4],q[0];\ny q[2];\ncz q[3],q[2];\ny q[0];\nh q[2];\ncz q[4],q[2];\ncz q[3],q[4];\ncz q[1],q[3];\nry(0.3253659522240325) q[3];\nx q[4];\nry(2.1448744966915387) q[4];\nrx(3.653797058759521) q[4];\nrx(4.5134000325238475) q[0];\ncx q[0],q[1];\ns q[3];\ncz q[3],q[1];\nt q[3];\ns q[2];\ncx q[2],q[3];\nrz(5.008883620445975) q[3];\ncx q[4],q[2];\nrx(3.9148371446715857) q[2];\ncx q[4],q[2];\ncx q[2],q[4];\nt q[4];\nx q[1];\ncz q[1],q[0];\nz q[4];\ncx q[2],q[3];\nry(1.8554306488512342) q[2];\ny q[1];\nh q[1];\ns q[4];\ncx q[4],q[2];\ns q[3];\ncx q[3],q[2];\ncx q[1],q[2];\nt q[2];\nt q[2];\nh q[2];\ns q[1];\nt q[0];\ncx q[2],q[1];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00000> -> (0.3425+0.0341i)|00000> + (-0.0700+0.0634i)|00001> + (0.2112+0.0872i)|00010> + (0.1291-0.0837i)|00011> + (-0.2826+0.0107i)|00100> + (-0.1041+0.0677i)|00101> + (0.2572+0.1436i)|00110> + (-0.0931+0.0854i)|00111> + (-0.1112+0.1141i)|01000> + (-0.0719-0.0293i)|01001> + (-0.0587-0.1959i)|01010> + (0.0299+0.0032i)|01011> + (0.0844-0.0905i)|01100> + (-0.0744-0.0473i)|01101> + (-0.0480-0.2211i)|01110> + (-0.0317-0.0101i)|01111> + (-0.1351-0.0815i)|10000> + (0.0947-0.0540i)|10001> + (0.1478+0.2651i)|10010> + (0.1447+0.1025i)|10011> + (0.1071+0.0412i)|10100> + (0.1207-0.0499i)|10101> + (0.1275+0.3525i)|10110> + (-0.1230-0.0650i)|10111> + (-0.1323+0.1325i)|11000> + (0.0578-0.0015i)|11001> + (-0.0160-0.0221i)|11010> + (0.0345+0.1086i)|11011> + (0.1011-0.1387i)|11100> + (0.0713-0.0050i)|11101> + (-0.0390-0.0135i)|11110> + (-0.0398-0.0926i)|11111>\n  |00001> -> (0.0166-0.1665i)|00000> + (-0.1304-0.1440i)|00001> + (0.0424-0.1027i)|00010> + (0.1722+0.2655i)|00011> + (0.0052+0.1374i)|00100> + (-0.1393-0.2141i)|00101> + (0.0698-0.1250i)|00110> + (-0.1756-0.1916i)|00111> + (0.0555+0.0541i)|01000> + (0.0603-0.1480i)|01001> + (-0.0952+0.0286i)|01010> + (-0.0065+0.0616i)|01011> + (-0.0440-0.0410i)|01100> + (0.0973-0.1532i)|01101> + (-0.1075+0.0233i)|01110> + (0.0208-0.0651i)|01111> + (-0.0396+0.0657i)|10000> + (0.1112+0.1948i)|10001> + (0.1289-0.0719i)|10010> + (-0.2108+0.2976i)|10011> + (0.0200-0.0521i)|10100> + (0.1027+0.2484i)|10101> + (0.1714-0.0620i)|10110> + (0.1337-0.2531i)|10111> + (0.0644+0.0643i)|11000> + (0.0031+0.1189i)|11001> + (-0.0107+0.0078i)|11010> + (-0.2234+0.0709i)|11011> + (-0.0674-0.0492i)|11100> + (0.0103+0.1468i)|11101> + (-0.0066+0.0190i)|11110> + (0.1904-0.0819i)|11111>\n  |00010> -> (-0.0197-0.2107i)|00000> + (-0.1275-0.1542i)|00001> + (0.0972+0.0904i)|00010> + (-0.3064-0.0048i)|00011> + (-0.0446-0.1681i)|00100> + (0.1400+0.2167i)|00101> + (-0.1073-0.1374i)|00110> + (-0.2498+0.0305i)|00111> + (-0.0473+0.0159i)|01000> + (0.0050+0.1745i)|01001> + (-0.0803+0.0803i)|01010> + (0.1123+0.0772i)|01011> + (-0.0253+0.0140i)|01100> + (0.0167-0.2025i)|01101> + (0.0942-0.0731i)|01110> + (0.0947+0.0721i)|01111> + (0.1219-0.0741i)|10000> + (-0.0757-0.1520i)|10001> + (0.0642-0.2095i)|10010> + (0.0882+0.2840i)|10011> + (0.0886-0.0652i)|10100> + (0.0568+0.1941i)|10101> + (-0.1144+0.2446i)|10110> + (0.1023+0.2075i)|10111> + (0.1555+0.0282i)|11000> + (0.0047+0.0228i)|11001> + (-0.0078-0.0800i)|11010> + (0.1057-0.1273i)|11011> + (0.1392+0.0112i)|11100> + (-0.0265-0.0256i)|11101> + (0.0141+0.0981i)|11110> + (0.0780-0.1303i)|11111>\n  |00011> -> (0.2764-0.0258i)|00000> + (-0.1176+0.0972i)|00001> + (-0.1186+0.1275i)|00010> + (-0.0036+0.2336i)|00011> + (0.2204-0.0585i)|00100> + (0.1652-0.1068i)|00101> + (0.1802-0.1407i)|00110> + (0.0233+0.1905i)|00111> + (-0.0208-0.0621i)|01000> + (0.1331-0.0038i)|01001> + (-0.1053-0.1052i)|01010> + (0.0589-0.0856i)|01011> + (-0.0184-0.0332i)|01100> + (-0.1544-0.0128i)|01101> + (0.0959+0.1235i)|01110> + (0.0550-0.0722i)|01111> + (0.0972+0.1599i)|10000> + (-0.1159+0.0577i)|10001> + (0.2747+0.0842i)|10010> + (0.2165-0.0673i)|10011> + (0.0854+0.1162i)|10100> + (0.1480-0.0433i)|10101> + (-0.3208-0.1500i)|10110> + (0.1582-0.0780i)|10111> + (-0.0369+0.2040i)|11000> + (0.0174-0.0036i)|11001> + (0.1049-0.0103i)|11010> + (-0.0970-0.0806i)|11011> + (-0.0146+0.1826i)|11100> + (-0.0195+0.0202i)|11101> + (-0.1287+0.0185i)|11110> + (-0.0994-0.0595i)|11111>\n  |00100> -> (-0.2786-0.1503i)|00000> + (0.1104-0.0121i)|00001> + (0.1890-0.0453i)|00010> + (0.0945-0.1381i)|00011> + (0.2460+0.0838i)|00100> + (0.1432+0.0012i)|00101> + (0.2547-0.0195i)|00110> + (-0.0614+0.1230i)|00111> + (0.0509+0.0353i)|01000> + (0.0972+0.0207i)|01001> + (-0.0182-0.1588i)|01010> + (0.0208-0.0746i)|01011> + (-0.0472-0.0495i)|01100> + (0.1055+0.0311i)|01101> + (0.0118-0.1811i)|01110> + (-0.0149+0.0583i)|01111> + (-0.1598-0.3278i)|10000> + (0.1476-0.0012i)|10001> + (-0.1910-0.1175i)|10010> + (-0.0766-0.0032i)|10011> + (0.1578+0.2387i)|10100> + (0.1801+0.0279i)|10101> + (-0.2093-0.1686i)|10110> + (0.0553-0.0074i)|10111> + (-0.1619+0.1695i)|11000> + (0.0120+0.0057i)|11001> + (0.1058+0.0543i)|11010> + (-0.0256-0.0873i)|11011> + (0.1277-0.1633i)|11100> + (0.0198-0.0033i)|11101> + (0.1337+0.0614i)|11110> + (0.0355+0.0755i)|11111>\n  |00101> -> (-0.0730+0.1354i)|00000> + (0.0249+0.2272i)|00001> + (-0.0220-0.0919i)|00010> + (0.2841+0.1943i)|00011> + (0.0407-0.1196i)|00100> + (-0.0025+0.2946i)|00101> + (-0.0095-0.1238i)|00110> + (-0.2530-0.1263i)|00111> + (0.0171-0.0248i)|01000> + (-0.0425+0.2000i)|01001> + (-0.0772+0.0088i)|01010> + (0.1535+0.0428i)|01011> + (-0.0241+0.0229i)|01100> + (-0.0641+0.2170i)|01101> + (-0.0880-0.0057i)|01110> + (-0.1199-0.0306i)|01111> + (-0.1594+0.0777i)|10000> + (0.0024+0.3035i)|10001> + (-0.0571+0.0929i)|10010> + (0.0066-0.1576i)|10011> + (0.1161-0.0767i)|10100> + (-0.0574+0.3705i)|10101> + (-0.0820+0.1017i)|10110> + (0.0153+0.1137i)|10111> + (0.0824+0.0787i)|11000> + (-0.0117+0.0247i)|11001> + (0.0264-0.0514i)|11010> + (0.1797-0.0527i)|11011> + (-0.0794-0.0621i)|11100> + (0.0069+0.0407i)|11101> + (0.0299-0.0650i)|11110> + (-0.1553+0.0731i)|11111>\n  |00110> -> (0.1090+0.2067i)|00000> + (0.1688+0.0428i)|00001> + (0.0288+0.1498i)|00010> + (-0.2548-0.1101i)|00011> + (0.1118+0.1559i)|00100> + (-0.2099-0.0906i)|00101> + (-0.0143-0.1962i)|00110> + (-0.2215-0.0545i)|00111> + (0.0468+0.0927i)|01000> + (-0.0419-0.1429i)|01001> + (-0.1149+0.0672i)|01010> + (0.0445-0.0481i)|01011> + (0.0370+0.0829i)|01100> + (0.0248+0.1544i)|01101> + (0.1416-0.0630i)|01110> + (0.0203-0.0321i)|01111> + (0.0449-0.2222i)|10000> + (-0.2006-0.2057i)|10001> + (-0.0739+0.1062i)|10010> + (0.0936-0.1621i)|10011> + (0.0076-0.1762i)|10100> + (0.2094+0.2856i)|10101> + (0.1090-0.1090i)|10110> + (0.0609-0.1308i)|10111> + (0.1238+0.0241i)|11000> + (0.0593+0.0871i)|11001> + (-0.0052+0.0170i)|11010> + (-0.1303+0.1612i)|11011> + (0.1157+0.0045i)|11100> + (-0.0780-0.1040i)|11101> + (-0.0084-0.0268i)|11110> + (-0.1005+0.1531i)|11111>\n  |00111> -> (-0.2711+0.1429i)|00000> + (0.0327-0.1287i)|00001> + (-0.1965+0.0378i)|00010> + (-0.0839+0.1943i)|00011> + (-0.2045+0.1467i)|00100> + (-0.0691+0.1601i)|00101> + (0.2573-0.0188i)|00110> + (-0.0415+0.1689i)|00111> + (-0.1216+0.0614i)|01000> + (-0.1090+0.0319i)|01001> + (-0.0882-0.1507i)|01010> + (-0.0367-0.0339i)|01011> + (-0.1087+0.0485i)|01100> + (0.1177-0.0189i)|01101> + (0.0826+0.1857i)|01110> + (-0.0245-0.0155i)|01111> + (0.2915+0.0589i)|10000> + (-0.1569+0.1529i)|10001> + (-0.1393-0.0970i)|10010> + (-0.1236-0.0714i)|10011> + (0.2311+0.0099i)|10100> + (0.2178-0.1597i)|10101> + (0.1430+0.1430i)|10110> + (-0.0997-0.0465i)|10111> + (-0.0317+0.1624i)|11000> + (0.0664-0.0452i)|11001> + (-0.0223-0.0068i)|11010> + (0.1229+0.0994i)|11011> + (-0.0059+0.1518i)|11100> + (-0.0793+0.0595i)|11101> + (0.0352-0.0110i)|11110> + (0.1168+0.0766i)|11111>\n  |01000> -> (0.0293-0.0031i)|00000> + (0.0943+0.0322i)|00001> + (-0.1047-0.1252i)|00010> + (0.0103-0.0658i)|00011> + (-0.0279+0.0279i)|00100> + (0.1058+0.0448i)|00101> + (-0.1228-0.1511i)|00110> + (0.0034+0.0634i)|00111> + (0.0770-0.2212i)|01000> + (-0.0763-0.0328i)|01001> + (0.1841-0.1873i)|01010> + (-0.0359+0.1917i)|01011> + (-0.0454+0.1796i)|01100> + (-0.0821-0.0569i)|01101> + (0.2715-0.1971i)|01110> + (0.0081-0.1573i)|01111> + (0.0133+0.2306i)|10000> + (0.0237+0.0017i)|10001> + (0.1410-0.0281i)|10010> + (-0.0309-0.0839i)|10011> + (-0.0294-0.1939i)|10100> + (0.0301+0.0162i)|10101> + (0.1454-0.0078i)|10110> + (0.0264+0.0735i)|10111> + (-0.2681+0.1020i)|11000> + (-0.0699+0.1008i)|11001> + (0.2819-0.0257i)|11010> + (-0.0845+0.0920i)|11011> + (0.1986-0.1210i)|11100> + (-0.1018+0.1166i)|11101> + (0.3476+0.0113i)|11110> + (0.0512-0.0821i)|11111>\n  |01001> -> (-0.0015-0.0143i)|00000> + (-0.0663+0.1941i)|00001> + (-0.0609+0.0509i)|00010> + (0.1353+0.0211i)|00011> + (0.0136+0.0136i)|00100> + (-0.0922+0.2176i)|00101> + (-0.0734+0.0597i)|00110> + (-0.1305+0.0070i)|00111> + (-0.1075-0.0374i)|01000> + (0.0674-0.1569i)|01001> + (-0.0911-0.0895i)|01010> + (-0.3944-0.0739i)|01011> + (0.0873+0.0221i)|01100> + (0.1171-0.1689i)|01101> + (-0.0958-0.1320i)|01110> + (0.3237+0.0167i)|01111> + (0.1121-0.0065i)|10000> + (-0.0034+0.0487i)|10001> + (-0.0136-0.0685i)|10010> + (0.1726-0.0636i)|10011> + (-0.0943+0.0143i)|10100> + (-0.0334+0.0619i)|10101> + (-0.0038-0.0707i)|10110> + (-0.1512+0.0543i)|10111> + (0.0496+0.1303i)|11000> + (-0.2074-0.1437i)|11001> + (-0.0125-0.1370i)|11010> + (-0.1892-0.1738i)|11011> + (-0.0588-0.0965i)|11100> + (-0.2400-0.2094i)|11101> + (0.0055-0.1690i)|11110> + (0.1689+0.1054i)|11111>\n  |01010> -> (-0.0734-0.0561i)|00000> + (0.0313+0.1407i)|00001> + (0.0338-0.1342i)|00010> + (-0.0247+0.0067i)|00011> + (-0.0795-0.0377i)|00100> + (-0.0349-0.1686i)|00101> + (-0.0497+0.1513i)|00110> + (-0.0216+0.0281i)|00111> + (0.1652+0.0760i)|01000> + (-0.0815+0.0638i)|01001> + (-0.1937+0.0297i)|01010> + (-0.2769+0.1875i)|01011> + (0.1428+0.0471i)|01100> + (0.1246-0.0592i)|01101> + (0.2435+0.0039i)|01110> + (-0.1986+0.1750i)|01111> + (-0.1094+0.0645i)|10000> + (-0.0960-0.0688i)|10001> + (-0.0466-0.0139i)|10010> + (0.1413-0.1431i)|10011> + (-0.0858+0.0555i)|10100> + (0.0890+0.0997i)|10101> + (0.0372+0.0109i)|10110> + (0.1183-0.1352i)|10111> + (0.0577+0.1610i)|11000> + (-0.2296-0.0957i)|11001> + (0.1489+0.0850i)|11010> + (0.2312-0.1102i)|11011> + (0.0669+0.1143i)|11100> + (0.2654+0.1512i)|11101> + (-0.1748-0.1276i)|11110> + (0.1679-0.1220i)|11111>\n  |01011> -> (0.0736-0.0962i)|00000> + (0.1073-0.0239i)|00001> + (0.1759+0.0443i)|00010> + (0.0051+0.0189i)|00011> + (0.0494-0.1042i)|00100> + (-0.1286+0.0266i)|00101> + (-0.1984-0.0652i)|00110> + (0.0215+0.0165i)|00111> + (-0.0997+0.2167i)|01000> + (0.0486+0.0621i)|01001> + (-0.0389-0.2540i)|01010> + (0.1430+0.2112i)|01011> + (-0.0618+0.1873i)|01100> + (-0.0451-0.0950i)|01101> + (-0.0051+0.3193i)|01110> + (0.1334+0.1514i)|01111> + (-0.0845-0.1435i)|10000> + (-0.0525+0.0732i)|10001> + (0.0183-0.0611i)|10010> + (-0.1091-0.1077i)|10011> + (-0.0728-0.1126i)|10100> + (0.0760-0.0679i)|10101> + (-0.0143+0.0487i)|10110> + (-0.1031-0.0902i)|10111> + (-0.2112+0.0757i)|11000> + (-0.0729+0.1750i)|11001> + (-0.1115+0.1953i)|11010> + (-0.0840-0.1763i)|11011> + (-0.1500+0.0878i)|11100> + (0.1153-0.2024i)|11101> + (0.1674-0.2292i)|11110> + (-0.0930-0.1281i)|11111>\n  |01100> -> (-0.1288+0.0464i)|00000> + (-0.0739-0.0290i)|00001> + (-0.1384-0.1513i)|00010> + (0.0055-0.0132i)|00011> + (0.1111-0.0688i)|00100> + (-0.0876-0.0358i)|00101> + (-0.1466-0.1853i)|00110> + (0.0054+0.0184i)|00111> + (-0.2542+0.3105i)|01000> + (0.0369+0.1222i)|01001> + (-0.0162-0.1700i)|01010> + (0.0188+0.1123i)|01011> + (0.1701-0.2759i)|01100> + (0.0207+0.1618i)|01101> + (0.0217-0.2044i)|01110> + (-0.0225-0.0872i)|01111> + (-0.0271+0.1819i)|10000> + (0.0209-0.0667i)|10001> + (-0.0204-0.0444i)|10010> + (0.0595+0.0952i)|10011> + (0.0250-0.1587i)|10100> + (0.0306-0.0638i)|10101> + (-0.0005-0.0704i)|10110> + (-0.0578-0.0758i)|10111> + (-0.2494-0.0616i)|11000> + (-0.1142+0.0768i)|11001> + (-0.2256+0.1129i)|11010> + (0.0191-0.1381i)|11011> + (0.1988+0.0114i)|11100> + (-0.1509+0.0763i)|11101> + (-0.2989+0.1100i)|11110> + (0.0053+0.1129i)|11111>\n  |01101> -> (0.0226+0.0626i)|00000> + (0.0596-0.1520i)|00001> + (-0.0736+0.0673i)|00010> + (0.0272+0.0113i)|00011> + (-0.0334-0.0540i)|00100> + (0.0736-0.1802i)|00101> + (-0.0901+0.0713i)|00110> + (-0.0379+0.0111i)|00111> + (0.1509+0.1236i)|01000> + (-0.2514+0.0759i)|01001> + (-0.0826+0.0079i)|01010> + (-0.2310+0.0387i)|01011> + (-0.1341-0.0827i)|01100> + (-0.3328+0.0426i)|01101> + (-0.0994-0.0105i)|01110> + (0.1793-0.0464i)|01111> + (0.0884+0.0132i)|10000> + (0.1372+0.0431i)|10001> + (-0.0216+0.0099i)|10010> + (-0.1959+0.1224i)|10011> + (-0.0772-0.0121i)|10100> + (0.1313+0.0629i)|10101> + (-0.0342+0.0002i)|10110> + (0.1560-0.1189i)|10111> + (-0.0299+0.1212i)|11000> + (-0.1579-0.2349i)|11001> + (0.0549+0.1097i)|11010> + (0.2841+0.0392i)|11011> + (0.0055-0.0966i)|11100> + (-0.1570-0.3103i)|11101> + (0.0535+0.1453i)|11110> + (-0.2323+0.0108i)|11111>\n  |01110> -> (0.0135+0.0141i)|00000> + (-0.0456-0.1756i)|00001> + (0.0306-0.1056i)|00010> + (-0.1108+0.0491i)|00011> + (0.0267+0.0042i)|00100> + (0.0381+0.2054i)|00101> + (-0.0384+0.1256i)|00110> + (-0.0934+0.0677i)|00111> + (-0.2539+0.0241i)|01000> + (0.0878-0.2415i)|01001> + (-0.0725-0.0312i)|01010> + (-0.2379+0.0165i)|01011> + (-0.1969+0.0443i)|01100> + (-0.1578+0.2777i)|01101> + (0.0852+0.0617i)|01110> + (-0.1940+0.0357i)|01111> + (-0.1469+0.0440i)|10000> + (-0.0454+0.0449i)|10001> + (-0.0109+0.0894i)|10010> + (-0.0853+0.1430i)|10011> + (-0.1286+0.0471i)|10100> + (0.0359-0.0359i)|10101> + (0.0341-0.0961i)|10110> + (-0.0638+0.1179i)|10111> + (0.1584+0.1143i)|11000> + (-0.2248-0.0040i)|11001> + (-0.1185-0.1480i)|11010> + (-0.2216-0.0350i)|11011> + (0.1431+0.0677i)|11100> + (0.2814+0.0368i)|11101> + (0.1222+0.1983i)|11110> + (-0.1737+0.0050i)|11111>\n  |01111> -> (-0.0185+0.0177i)|00000> + (-0.1339+0.0348i)|00001> + (0.1385+0.0401i)|00010> + (0.0374+0.0845i)|00011> + (-0.0055+0.0351i)|00100> + (0.1566-0.0290i)|00101> + (-0.1647-0.0504i)|00110> + (0.0516+0.0712i)|00111> + (-0.0316-0.3330i)|01000> + (-0.1841-0.0669i)|01001> + (0.0409-0.0951i)|01010> + (0.0126+0.1814i)|01011> + (-0.0581-0.2582i)|01100> + (0.2117+0.1203i)|01101> + (-0.0809+0.1118i)|01110> + (0.0273+0.1479i)|01111> + (-0.0577-0.1926i)|10000> + (0.0342+0.0346i)|10001> + (-0.1173-0.0143i)|10010> + (0.1091+0.0650i)|10011> + (-0.0617-0.1687i)|10100> + (-0.0274-0.0274i)|10101> + (0.1260+0.0447i)|10110> + (0.0899+0.0486i)|10111> + (-0.1499+0.2077i)|11000> + (-0.0031+0.1714i)|11001> + (0.1941-0.1555i)|11010> + (-0.0267+0.1690i)|11011> + (-0.0888+0.1876i)|11100> + (0.0281-0.2146i)|11101> + (-0.2601+0.1602i)|11110> + (0.0038+0.1324i)|11111>\n  |10000> -> (0.1772-0.1999i)|00000> + (-0.0255-0.1468i)|00001> + (-0.2396+0.2128i)|00010> + (0.0171-0.1295i)|00011> + (0.1801-0.2782i)|00100> + (0.0091+0.1250i)|00101> + (0.2107-0.1542i)|00110> + (-0.0041-0.1574i)|00111> + (0.0817+0.0951i)|01000> + (0.0766-0.0191i)|01001> + (0.1268+0.0363i)|01010> + (-0.0285+0.0107i)|01011> + (0.1073+0.1196i)|01100> + (-0.0670+0.0008i)|01101> + (-0.0746-0.0497i)|01110> + (-0.0269+0.0030i)|01111> + (-0.1532+0.0964i)|10000> + (-0.0100+0.1174i)|10001> + (-0.3876-0.0639i)|10010> + (0.1393-0.0697i)|10011> + (-0.1685+0.1268i)|10100> + (0.0230-0.0904i)|10101> + (0.3103+0.0984i)|10110> + (0.1603-0.1032i)|10111> + (-0.0419+0.1098i)|11000> + (0.0143+0.0622i)|11001> + (-0.0320-0.0952i)|11010> + (0.0514+0.0259i)|11011> + (-0.0080+0.1391i)|11100> + (-0.0134-0.0460i)|11101> + (0.0365+0.0883i)|11110> + (0.0766+0.0166i)|11111>\n  |10001> -> (-0.0972-0.0861i)|00000> + (0.3020-0.0524i)|00001> + (0.1035+0.1165i)|00010> + (0.2664+0.0352i)|00011> + (-0.1352-0.0875i)|00100> + (-0.2571+0.0187i)|00101> + (-0.0749-0.1024i)|00110> + (0.3237-0.0084i)|00111> + (0.0462-0.0397i)|01000> + (0.0394+0.1576i)|01001> + (0.0176-0.0616i)|01010> + (-0.0220-0.0587i)|01011> + (0.0581-0.0522i)|01100> + (-0.0017-0.1378i)|01101> + (-0.0241+0.0362i)|01110> + (-0.0061-0.0553i)|01111> + (0.0469+0.0745i)|10000> + (-0.2415-0.0206i)|10001> + (-0.0311+0.1884i)|10010> + (0.1433+0.2865i)|10011> + (0.0616+0.0819i)|10100> + (0.1860+0.0474i)|10101> + (0.0478-0.1508i)|10110> + (0.2123+0.3297i)|10111> + (0.0534+0.0204i)|11000> + (-0.1280+0.0294i)|11001> + (-0.0463+0.0156i)|11010> + (-0.0533+0.1056i)|11011> + (0.0676+0.0039i)|11100> + (0.0947-0.0277i)|11101> + (0.0429-0.0177i)|11110> + (-0.0342+0.1575i)|11111>\n  |10010> -> (-0.1466-0.1037i)|00000> + (0.2726-0.0669i)|00001> + (-0.2019+0.0530i)|00010> + (-0.1424+0.1910i)|00011> + (0.1940+0.0957i)|00100> + (0.2262-0.0334i)|00101> + (-0.1733+0.0274i)|00110> + (0.1392-0.2607i)|00111> + (0.0055+0.0832i)|01000> + (-0.1355-0.0874i)|01001> + (0.0192-0.0665i)|01010> + (0.0111-0.0571i)|01011> + (-0.0092-0.0923i)|01100> + (-0.0882-0.0859i)|01101> + (0.0384-0.0446i)|01110> + (-0.0298+0.0831i)|01111> + (-0.0271-0.1197i)|10000> + (0.1899+0.0672i)|10001> + (0.1689+0.2116i)|10010> + (0.2745+0.0679i)|10011> + (0.0446+0.1461i)|10100> + (0.1466+0.0837i)|10101> + (0.1120+0.1892i)|10110> + (-0.3360-0.0440i)|10111> + (0.0655-0.0466i)|11000> + (-0.0141+0.0889i)|11001> + (0.0837-0.0264i)|11010> + (0.0284-0.0991i)|11011> + (-0.0704+0.0836i)|11100> + (-0.0080+0.0850i)|11101> + (0.0614-0.0236i)|11110> + (0.0038+0.1222i)|11111>\n  |10011> -> (0.1361-0.1922i)|00000> + (-0.0510-0.2079i)|00001> + (-0.0695-0.2647i)|00010> + (0.1457+0.1086i)|00011> + (-0.1255+0.2545i)|00100> + (-0.0255-0.1725i)|00101> + (-0.0359-0.2273i)|00110> + (-0.1988-0.1061i)|00111> + (-0.1092+0.0072i)|01000> + (-0.0666+0.1033i)|01001> + (0.0872+0.0252i)|01010> + (-0.0436-0.0084i)|01011> + (0.1211-0.0121i)|01100> + (-0.0655+0.0673i)|01101> + (0.0585+0.0504i)|01110> + (0.0633+0.0227i)|01111> + (0.1570-0.0356i)|10000> + (0.0512-0.1448i)|10001> + (-0.2774+0.2214i)|10010> + (0.0517-0.2093i)|10011> + (-0.1916+0.0585i)|10100> + (0.0639-0.1118i)|10101> + (-0.2481+0.1469i)|10110> + (-0.0335+0.2562i)|10111> + (0.0612+0.0859i)|11000> + (0.0678+0.0107i)|11001> + (0.0346+0.1098i)|11010> + (-0.0756-0.0217i)|11011> + (-0.1096-0.0923i)|11100> + (0.0648+0.0061i)|11101> + (0.0310+0.0805i)|11110> + (0.0931-0.0029i)|11111>\n  |10100> -> (-0.2506+0.0971i)|00000> + (-0.0525+0.1467i)|00001> + (-0.0990+0.2901i)|00010> + (-0.0439-0.1222i)|00011> + (-0.2799+0.1628i)|00100> + (0.0539-0.1149i)|00101> + (0.1071-0.2345i)|00110> + (-0.0766-0.1417i)|00111> + (-0.0621-0.0089i)|01000> + (-0.0451+0.0456i)|01001> + (0.1102+0.1193i)|01010> + (-0.0570-0.0215i)|01011> + (-0.0515-0.0212i)|01100> + (0.0386-0.0202i)|01101> + (-0.0676-0.1201i)|01110> + (-0.0737-0.0259i)|01111> + (-0.3202-0.0118i)|10000> + (-0.1177+0.1504i)|10001> + (0.2218-0.0979i)|10010> + (-0.0428+0.0769i)|10011> + (-0.3911+0.0280i)|10100> + (0.1144-0.1093i)|10101> + (-0.1859+0.0478i)|10110> + (-0.0423+0.0934i)|10111> + (0.0039+0.1183i)|11000> + (0.0359+0.0331i)|11001> + (-0.0357+0.1263i)|11010> + (-0.0370-0.0435i)|11011> + (0.0456+0.1546i)|11100> + (-0.0361-0.0291i)|11101> + (0.0212-0.0963i)|11110> + (-0.0574-0.0358i)|11111>\n  |10101> -> (0.0472+0.1218i)|00000> + (-0.3017-0.1080i)|00001> + (0.1410+0.0481i)|00010> + (0.2514-0.0903i)|00011> + (0.0791+0.1361i)|00100> + (0.2364+0.1108i)|00101> + (-0.1140-0.0521i)|00110> + (0.2915-0.1576i)|00111> + (-0.0043+0.0302i)|01000> + (-0.0938-0.0927i)|01001> + (0.0580-0.0536i)|01010> + (0.0442-0.1173i)|01011> + (-0.0103+0.0250i)|01100> + (0.0416+0.0794i)|01101> + (-0.0584+0.0329i)|01110> + (0.0534-0.1515i)|01111> + (-0.0057+0.1556i)|10000> + (-0.3094-0.2421i)|10001> + (-0.0476-0.1078i)|10010> + (-0.1581-0.0881i)|10011> + (0.0136+0.1901i)|10100> + (0.2249+0.2352i)|10101> + (0.0232+0.0904i)|10110> + (-0.1921-0.0870i)|10111> + (0.0575-0.0019i)|11000> + (-0.0681+0.0738i)|11001> + (0.0614+0.0173i)|11010> + (0.0895-0.0762i)|11011> + (0.0751-0.0222i)|11100> + (0.0599-0.0744i)|11101> + (-0.0468-0.0103i)|11110> + (0.0737-0.1182i)|11111>\n  |10110> -> (0.1799+0.0253i)|00000> + (-0.1989+0.1881i)|00001> + (-0.2069-0.0551i)|00010> + (-0.2116+0.1033i)|00011> + (-0.2253+0.0023i)|00100> + (-0.1822+0.1406i)|00101> + (-0.1635-0.0605i)|00110> + (0.2323-0.1630i)|00111> + (0.0283-0.0342i)|01000> + (0.0644+0.0639i)|01001> + (0.0089-0.1226i)|01010> + (-0.0587-0.0923i)|01011> + (-0.0503+0.0447i)|01100> + (0.0271+0.0723i)|01101> + (0.0252-0.0905i)|01110> + (0.0687+0.1004i)|01111> + (-0.1587-0.1459i)|10000> + (0.3497-0.0611i)|10001> + (-0.0246-0.1516i)|10010> + (-0.1066-0.1207i)|10011> + (0.2086+0.1524i)|10100> + (0.2882-0.0097i)|10101> + (0.0024-0.1287i)|10110> + (0.1433+0.1400i)|10111> + (0.0767-0.0173i)|11000> + (-0.0797+0.0830i)|11001> + (-0.0420+0.0543i)|11010> + (0.0124+0.1047i)|11011> + (-0.0803+0.0473i)|11100> + (-0.0558+0.0658i)|11101> + (-0.0365+0.0539i)|11110> + (-0.0518-0.1336i)|11111>\n  |10111> -> (-0.0332+0.2360i)|00000> + (0.1434+0.1516i)|00001> + (0.0722-0.2713i)|00010> + (0.0788+0.1614i)|00011> + (-0.0030-0.2955i)|00100> + (0.1072+0.1389i)|00101> + (0.0793-0.2144i)|00110> + (-0.1243-0.1771i)|00111> + (0.0448+0.0371i)|01000> + (0.0487-0.0491i)|01001> + (0.1608+0.0116i)|01010> + (-0.0704+0.0448i)|01011> + (-0.0586-0.0660i)|01100> + (0.0551-0.0207i)|01101> + (0.1187+0.0330i)|01110> + (0.0766-0.0524i)|01111> + (0.1913-0.2082i)|10000> + (-0.0466-0.2666i)|10001> + (0.1988-0.0323i)|10010> + (-0.0920+0.0813i)|10011> + (-0.1999+0.2736i)|10100> + (-0.0074-0.2197i)|10101> + (0.1688+0.0031i)|10110> + (0.1068-0.1092i)|10111> + (0.0227+0.1006i)|11000> + (0.0633+0.0608i)|11001> + (-0.0713-0.0550i)|11010> + (0.0798-0.0095i)|11011> + (-0.0620-0.1053i)|11100> + (0.0502+0.0425i)|11101> + (-0.0707-0.0479i)|11110> + (-0.1019+0.0395i)|11111>\n  |11000> -> (0.1009-0.0021i)|00000> + (-0.0550+0.0582i)|00001> + (0.1204-0.0865i)|00010> + (-0.0012-0.0541i)|00011> + (0.0971-0.0093i)|00100> + (0.0454-0.0331i)|00101> + (-0.0858+0.0580i)|00110> + (-0.0174-0.0550i)|00111> + (-0.1410-0.1184i)|01000> + (0.1021-0.0332i)|01001> + (0.0633+0.3773i)|01010> + (0.1153+0.1082i)|01011> + (-0.1912-0.1337i)|01100> + (-0.0909+0.0134i)|01101> + (-0.0152-0.3202i)|01110> + (0.1590+0.1137i)|01111> + (0.1201+0.0667i)|10000> + (-0.0592+0.0291i)|10001> + (-0.0784+0.0355i)|10010> + (-0.0315+0.0144i)|10011> + (0.1732+0.0613i)|10100> + (0.0570-0.0223i)|10101> + (0.0829+0.0004i)|10110> + (-0.0512+0.0215i)|10111> + (-0.0900+0.2483i)|11000> + (-0.0769-0.1382i)|11001> + (-0.1469+0.3017i)|11010> + (0.0285+0.1241i)|11011> + (-0.0621+0.3067i)|11100> + (0.0496+0.1167i)|11101> + (0.1487-0.2228i)|11110> + (0.0503+0.1411i)|11111>\n  |11001> -> (-0.0010-0.0491i)|00000> + (-0.1196-0.1132i)|00001> + (-0.0420-0.0586i)|00010> + (0.1113-0.0024i)|00011> + (-0.0045-0.0472i)|00100> + (0.0681+0.0934i)|00101> + (0.0282+0.0417i)|00110> + (0.1131-0.0357i)|00111> + (-0.0576+0.0686i)|01000> + (0.0683+0.2101i)|01001> + (0.1834-0.0308i)|01010> + (-0.2226+0.2371i)|01011> + (-0.0650+0.0930i)|01100> + (-0.0275-0.1870i)|01101> + (-0.1557+0.0074i)|01110> + (-0.2340+0.3271i)|01111> + (0.0324-0.0584i)|10000> + (-0.0598-0.1218i)|10001> + (0.0173+0.0381i)|10010> + (-0.0295-0.0649i)|10011> + (0.0298-0.0842i)|10100> + (0.0460+0.1172i)|10101> + (0.0002-0.0403i)|10110> + (-0.0443-0.1054i)|10111> + (0.1207+0.0438i)|11000> + (0.2843-0.1581i)|11001> + (0.1466+0.0714i)|11010> + (-0.2553+0.0587i)|11011> + (0.1491+0.0302i)|11100> + (-0.2401+0.1021i)|11101> + (-0.1083-0.0723i)|11110> + (-0.2902+0.1036i)|11111>\n  |11010> -> (-0.0677-0.0339i)|00000> + (-0.1307+0.0185i)|00001> + (0.0863+0.0689i)|00010> + (-0.0879+0.0094i)|00011> + (0.0794+0.0148i)|00100> + (-0.0919+0.0102i)|00101> + (0.0505+0.0585i)|00110> + (0.0835-0.0152i)|00111> + (0.1078-0.0699i)|01000> + (0.0107-0.1850i)|01001> + (0.1323-0.2263i)|01010> + (0.0275+0.2830i)|01011> + (-0.1232+0.1085i)|01100> + (0.0261-0.1592i)|01101> + (0.1356-0.1716i)|01110> + (-0.0729-0.3425i)|01111> + (0.0281+0.0818i)|10000> + (0.1339+0.0162i)|10001> + (-0.0106+0.0324i)|10010> + (-0.0143-0.0752i)|10011> + (-0.0431-0.1062i)|10100> + (0.1128+0.0394i)|10101> + (-0.0137+0.0429i)|10110> + (0.0492+0.1077i)|10111> + (0.1691+0.0447i)|11000> + (0.2372-0.1739i)|11001> + (-0.1836+0.1236i)|11010> + (0.0615-0.2275i)|11011> + (-0.2036-0.0291i)|11100> + (0.2063-0.1119i)|11101> + (-0.1569+0.0830i)|11110> + (-0.0324+0.2775i)|11111>\n  |11011> -> (0.0445-0.0887i)|00000> + (0.0141+0.0996i)|00001> + (-0.0904+0.1132i)|00010> + (0.0072+0.0670i)|00011> + (-0.0194+0.1042i)|00100> + (0.0078+0.0701i)|00101> + (-0.0767+0.0663i)|00110> + (-0.0116-0.0637i)|00111> + (0.0917+0.1414i)|01000> + (-0.1411-0.0082i)|01001> + (0.2968+0.1736i)|01010> + (0.2158-0.0210i)|01011> + (-0.1423-0.1616i)|01100> + (-0.1214-0.0199i)|01101> + (0.2250+0.1778i)|01110> + (-0.2612+0.0556i)|01111> + (-0.1073+0.0368i)|10000> + (0.0124-0.1021i)|10001> + (-0.0426-0.0139i)|10010> + (-0.0573+0.0109i)|10011> + (0.1393-0.0566i)|10100> + (0.0301-0.0860i)|10101> + (-0.0563-0.0179i)|10110> + (0.0821-0.0375i)|10111> + (-0.0587+0.2218i)|11000> + (-0.1326-0.1809i)|11001> + (-0.1621-0.2407i)|11010> + (-0.1734-0.0469i)|11011> + (0.0382-0.2670i)|11100> + (-0.0854-0.1573i)|11101> + (-0.1089-0.2058i)|11110> + (0.2116+0.0247i)|11111>\n  |11100> -> (-0.0965+0.0556i)|00000> + (0.0312-0.0650i)|00001> + (0.1567-0.0506i)|00010> + (0.0227-0.0435i)|00011> + (-0.0820+0.0856i)|00100> + (-0.0231+0.0448i)|00101> + (-0.1146+0.0149i)|00110> + (0.0187-0.0435i)|00111> + (0.1011+0.3091i)|01000> + (-0.1757-0.0611i)|01001> + (0.1607+0.1515i)|01010> + (0.0878+0.0176i)|01011> + (0.1746+0.3623i)|01100> + (0.1401+0.0683i)|01101> + (-0.1139-0.1508i)|01110> + (0.1128+0.0124i)|01111> + (0.0711+0.0052i)|10000> + (-0.0032+0.0417i)|10001> + (0.1109+0.0781i)|10010> + (0.0668+0.0004i)|10011> + (0.1137+0.0117i)|10100> + (0.0195-0.0353i)|10101> + (-0.0966-0.0807i)|10110> + (0.0882-0.0143i)|10111> + (-0.1957+0.1741i)|11000> + (-0.0078-0.1629i)|11001> + (-0.0022-0.3253i)|11010> + (-0.0848-0.0963i)|11011> + (-0.2049+0.2302i)|11100> + (-0.0114+0.1297i)|11101> + (-0.0257+0.2596i)|11110> + (-0.1163-0.0981i)|11111>\n  |11101> -> (0.0270+0.0469i)|00000> + (0.1337+0.0642i)|00001> + (-0.0246-0.0762i)|00010> + (0.0896+0.0466i)|00011> + (0.0416+0.0399i)|00100> + (-0.0921-0.0475i)|00101> + (0.0072+0.0557i)|00110> + (0.0896+0.0385i)|00111> + (0.1503-0.0492i)|01000> + (0.1256-0.3614i)|01001> + (0.0736-0.0781i)|01010> + (-0.0361+0.1806i)|01011> + (0.1761-0.0849i)|01100> + (-0.1404+0.2882i)|01101> + (-0.0733+0.0553i)|01110> + (-0.0255+0.2320i)|01111> + (0.0025-0.0346i)|10000> + (-0.0859-0.0065i)|10001> + (0.0380-0.0539i)|10010> + (-0.0009+0.1374i)|10011> + (0.0057-0.0553i)|10100> + (0.0726+0.0401i)|10101> + (-0.0392+0.0469i)|10110> + (0.0294+0.1814i)|10111> + (0.0846+0.0951i)|11000> + (0.3352-0.0160i)|11001> + (-0.1581+0.0011i)|11010> + (0.1982-0.1746i)|11011> + (0.1119+0.0996i)|11100> + (-0.2669-0.0235i)|11101> + (0.1262+0.0125i)|11110> + (0.2017-0.2392i)|11111>\n  |11110> -> (0.0385+0.0553i)|00000> + (0.1427+0.0249i)|00001> + (0.0942+0.0354i)|00010> + (-0.0816+0.0565i)|00011> + (-0.0408-0.0503i)|00100> + (0.0950+0.0354i)|00101> + (0.0652+0.0268i)|00110> + (0.0670-0.0821i)|00111> + (-0.0852+0.1993i)|01000> + (0.1770+0.2947i)|01001> + (0.1277-0.0606i)|01010> + (-0.0800+0.1483i)|01011> + (0.0766-0.2558i)|01100> + (0.1120+0.2640i)|01101> + (0.1160-0.0408i)|01110> + (0.0734-0.2024i)|01111> + (-0.0179+0.0555i)|10000> + (0.0307+0.0326i)|10001> + (-0.0381-0.0955i)|10010> + (0.0838+0.0764i)|10011> + (0.0065-0.0900i)|10100> + (0.0408+0.0428i)|10101> + (-0.0149-0.0899i)|10110> + (-0.1165-0.0951i)|10111> + (0.1747-0.0422i)|11000> + (0.1334-0.2577i)|11001> + (0.2224-0.0295i)|11010> + (-0.1580+0.1664i)|11011> + (-0.1974+0.0799i)|11100> + (0.1283-0.1943i)|11101> + (0.1790+0.0006i)|11110> + (0.1617-0.2159i)|11111>\n  |11111> -> (-0.0725+0.0504i)|00000> + (0.0190-0.1088i)|00001> + (-0.0465+0.1235i)|00010> + (0.0431+0.0623i)|00011> + (0.0659-0.0534i)|00100> + (0.0270-0.0724i)|00101> + (-0.0351+0.0855i)|00110> + (-0.0626-0.0511i)|00111> + (-0.2614-0.1117i)|01000> + (0.2247-0.1350i)|01001> + (0.0794+0.1674i)|01010> + (0.1131+0.0610i)|01011> + (0.3355+0.1005i)|01100> + (0.2013-0.0854i)|01101> + (0.0535+0.1522i)|01110> + (-0.1543-0.0560i)|01111> + (-0.0728-0.0235i)|10000> + (0.0248-0.0234i)|10001> + (0.1252-0.0500i)|10010> + (0.0583-0.0639i)|10011> + (0.1181+0.0086i)|10100> + (0.0326-0.0311i)|10101> + (0.1178-0.0196i)|10110> + (-0.0725+0.0888i)|10111> + (0.0553+0.2291i)|11000> + (-0.1965-0.1017i)|11001> + (0.0387+0.2916i)|11010> + (0.1269+0.1204i)|11011> + (-0.1048-0.2589i)|11100> + (-0.1482-0.0978i)|11101> + (-0.0009+0.2347i)|11110> + (-0.1646-0.1233i)|11111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T4", "task_code": "B1_debugging", "task_name": "Debugging", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "The following 5-qubit quantum circuit has exactly ONE bug (a wrong gate, swapped qubits, or missing gate).\n\nBuggy circuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\nry(1.2991082020564804) q[4];\nx q[2];\ny q[3];\nrz(3.487754176137701) q[2];\nrx(0.643490595348736) q[4];\ns q[1];\ncz q[1],q[0];\nx q[3];\nt q[4];\ns q[1];\ncx q[2],q[0];\nt q[3];\nrz(4.13429172494234) q[1];\nry(4.808795900868258) q[1];\ncz q[3],q[1];\ncz q[3],q[0];\ncz q[1],q[0];\nrz(0.8874690506960367) q[0];\nt q[1];\ncz q[4],q[1];\nry(5.243404530617571) q[2];\ns q[1];\ny q[0];\nrx(4.1202803642574) q[0];\nrx(1.7512732600390188) q[1];\ny q[1];\nx q[1];\ncz q[2],q[3];\nh q[1];\ny q[1];\ncz q[0],q[1];\ncx q[4],q[0];\nrx(4.157377053192782) q[0];\nx q[2];\nx q[2];\ncz q[4],q[0];\ncz q[3],q[1];\nz q[3];\ny q[1];\nrx(4.637618986216838) q[3];\ny q[3];\nrx(2.938812261503058) q[2];\nz q[1];\ncx q[0],q[2];\nry(2.2883048916281914) q[0];\nt q[3];\ns q[1];\ncz q[0],q[2];\nry(2.3464623514216814) q[4];\nt q[3];\ncx q[4],q[2];\ncz q[1],q[4];\ncx q[4],q[3];\nh q[3];\nz q[3];\ns q[4];\nry(5.465220535694509) q[2];\nz q[0];\nry(0.6338373937239853) q[3];\nt q[2];\nt q[3];\ncz q[0],q[4];\nrx(3.2050737777115645) q[2];\ncz q[0],q[3];\nry(2.383270430564389) q[4];\ncz q[2],q[3];\n```\n\nThe INTENDED unitary transformation maps basis states as follows:\n  |00000> -> (-0.1645+0.0461i)|00000> + (-0.4943+0.1502i)|00001> + (-0.0337-0.0614i)|00010> + (-0.2364+0.1410i)|00011> + (-0.2256+0.1266i)|00100> + (0.0833-0.0236i)|00101> + (-0.1798-0.0990i)|00110> + (0.0560-0.1121i)|00111> + (-0.0430-0.0356i)|01000> + (0.1105+0.1216i)|01001> + (0.0136-0.0199i)|01010> + (0.0819+0.0216i)|01011> + (0.0792+0.0339i)|01100> + (0.0269+0.0197i)|01101> + (0.0232+0.0728i)|01110> + (0.0397-0.0057i)|01111> + (-0.0496-0.0409i)|10000> + (0.2349-0.2416i)|10001> + (-0.0443-0.1723i)|10010> + (-0.2618+0.0753i)|10011> + (-0.1487-0.0161i)|10100> + (0.0870+0.0709i)|10101> + (-0.2804+0.0077i)|10110> + (0.1510-0.1654i)|10111> + (-0.0158-0.0156i)|11000> + (-0.0918+0.0031i)|11001> + (0.0472-0.0491i)|11010> + (0.0794+0.0813i)|11011> + (0.0525+0.0218i)|11100> + (0.0163+0.0355i)|11101> + (0.0490+0.0914i)|11110> + (0.0861+0.0176i)|11111>\n  |00001> -> (-0.0170+0.0702i)|00000> + (-0.1600+0.1907i)|00001> + (-0.0636+0.0379i)|00010> + (-0.4707-0.0872i)|00011> + (0.2657-0.0163i)|00100> + (-0.0305-0.0651i)|00101> + (0.1302+0.2814i)|00110> + (0.0659-0.0055i)|00111> + (-0.0190+0.0103i)|01000> + (0.0526+0.0009i)|01001> + (-0.0299+0.0096i)|01010> + (0.1185+0.1069i)|01011> + (-0.0606-0.0690i)|01100> + (-0.0058-0.0136i)|01101> + (0.0148-0.1101i)|01110> + (0.0296+0.0067i)|01111> + (0.0070+0.0505i)|10000> + (0.2650+0.2283i)|10001> + (0.1831+0.0504i)|10010> + (-0.0293+0.2214i)|10011> + (0.1534+0.1232i)|10100> + (-0.2639-0.0209i)|10101> + (0.2445-0.0683i)|10110> + (-0.1002-0.1519i)|10111> + (-0.0076+0.0214i)|11000> + (-0.0270-0.1383i)|11001> + (0.0214+0.0601i)|11010> + (0.0556-0.0086i)|11011> + (-0.0372-0.0609i)|11100> + (-0.0782-0.0635i)|11101> + (-0.0494-0.0608i)|11110> + (0.0238-0.0567i)|11111>\n  |00010> -> (-0.0556-0.0249i)|00000> + (0.2586-0.0967i)|00001> + (-0.0733-0.0670i)|00010> + (-0.3268-0.0252i)|00011> + (-0.2117-0.0376i)|00100> + (-0.0888+0.0061i)|00101> + (-0.2587-0.4150i)|00110> + (-0.0263-0.0948i)|00111> + (-0.0150-0.0047i)|01000> + (-0.0790-0.0487i)|01001> + (-0.0093-0.0337i)|01010> + (0.0890+0.0439i)|01011> + (0.0206+0.0354i)|01100> + (-0.0195-0.0197i)|01101> + (0.0146+0.1492i)|01110> + (0.0067-0.0338i)|01111> + (-0.2381+0.1241i)|10000> + (0.1681+0.0467i)|10001> + (-0.0548+0.0481i)|10010> + (0.2796+0.0571i)|10011> + (-0.0599+0.3653i)|10100> + (-0.0547+0.0076i)|10101> + (0.0731+0.2470i)|10110> + (-0.0629+0.0589i)|10111> + (-0.1007-0.0118i)|11000> + (-0.0549-0.0361i)|11001> + (-0.0196-0.0096i)|11010> + (-0.0493-0.0752i)|11011> + (0.1068-0.0996i)|11100> + (-0.0234-0.0064i)|11101> + (0.0265-0.0656i)|11110> + (-0.0238-0.0062i)|11111>\n  |00011> -> (-0.0742-0.0313i)|00000> + (0.2150+0.0823i)|00001> + (-0.1488+0.0294i)|00010> + (-0.1944-0.1032i)|00011> + (-0.2785+0.4455i)|00100> + (-0.0996+0.1265i)|00101> + (0.0256+0.2886i)|00110> + (0.0937+0.0724i)|00111> + (-0.0079-0.0315i)|01000> + (-0.0239-0.0771i)|01001> + (-0.0365-0.0251i)|01010> + (0.0353+0.0377i)|01011> + (0.1650+0.0181i)|01100> + (-0.0542-0.0043i)|01101> + (0.0314-0.0596i)|01110> + (0.0077+0.0317i)|01111> + (-0.0112-0.1229i)|10000> + (0.0827+0.1716i)|10001> + (-0.1429-0.0441i)|10010> + (0.3003-0.0646i)|10011> + (0.0262-0.3200i)|10100> + (-0.0784-0.0267i)|10101> + (-0.2975-0.0432i)|10110> + (-0.0084+0.0677i)|10111> + (0.0163-0.0393i)|11000> + (-0.0053-0.0684i)|11001> + (-0.0143-0.0619i)|11010> + (-0.0918-0.0667i)|11011> + (-0.0660+0.0555i)|11100> + (-0.0213-0.0136i)|11101> + (0.0668+0.1030i)|11110> + (-0.0288+0.0156i)|11111>\n  |00100> -> (-0.2989+0.1200i)|00000> + (-0.0221-0.0446i)|00001> + (-0.1685-0.2151i)|00010> + (-0.0153+0.0413i)|00011> + (-0.0195-0.0833i)|00100> + (-0.0432+0.1341i)|00101> + (0.0400-0.0501i)|00110> + (-0.1917+0.3929i)|00111> + (-0.0846-0.0598i)|01000> + (0.0104+0.0155i)|01001> + (-0.0085-0.0625i)|01010> + (-0.0019-0.0101i)|01011> + (-0.0162+0.0188i)|01100> + (-0.0650+0.0245i)|01101> + (-0.0121+0.0176i)|01110> + (-0.0965+0.0576i)|01111> + (-0.0466-0.0768i)|10000> + (-0.2373-0.1277i)|10001> + (0.2819-0.0846i)|10010> + (-0.0357-0.1850i)|10011> + (-0.0236-0.0096i)|10100> + (-0.3980+0.0616i)|10101> + (-0.1259+0.1471i)|10110> + (-0.2333-0.1812i)|10111> + (-0.0144-0.0178i)|11000> + (0.0474+0.0890i)|11001> + (0.1005+0.0614i)|11010> + (-0.0458+0.0504i)|11011> + (0.0083+0.0125i)|11100> + (-0.1312-0.0533i)|11101> + (0.0675+0.0039i)|11110> + (-0.0139-0.1282i)|11111>\n  |00101> -> (-0.1153+0.2765i)|00000> + (0.0261+0.0755i)|00001> + (-0.0024+0.0571i)|00010> + (0.0856-0.0627i)|00011> + (0.0129-0.1746i)|00100> + (0.0962+0.4902i)|00101> + (0.0487-0.0076i)|00110> + (0.0637-0.0449i)|00111> + (-0.0903+0.0183i)|01000> + (0.0072-0.0209i)|01001> + (0.0114+0.0233i)|01010> + (-0.0328-0.0140i)|01011> + (-0.0489+0.0282i)|01100> + (-0.1023+0.0818i)|01101> + (-0.0049-0.0151i)|01110> + (0.0391+0.0195i)|01111> + (-0.0246+0.0222i)|10000> + (0.0975+0.0641i)|10001> + (0.0170-0.3438i)|10010> + (0.2152-0.0908i)|10011> + (0.0468-0.0242i)|10100> + (0.2074-0.2938i)|10101> + (0.1690+0.0751i)|10110> + (0.2020-0.3197i)|10111> + (-0.0127+0.0219i)|11000> + (-0.0195-0.0433i)|11001> + (0.1027-0.0666i)|11010> + (-0.0731-0.0527i)|11011> + (-0.0157+0.0091i)|11100> + (0.1397-0.0167i)|11101> + (-0.0114-0.0692i)|11110> + (0.1382+0.0003i)|11111>\n  |00110> -> (-0.2906+0.4085i)|00000> + (0.1332-0.1031i)|00001> + (0.3061+0.1059i)|00010> + (-0.0319-0.1254i)|00011> + (-0.0579-0.0396i)|00100> + (-0.0609-0.2953i)|00101> + (-0.0817+0.1329i)|00110> + (-0.1260-0.2742i)|00111> + (-0.1295-0.0153i)|01000> + (-0.0525-0.0183i)|01001> + (0.0707+0.0918i)|01010> + (-0.0156+0.0367i)|01011> + (0.0077+0.0181i)|01100> + (0.0659-0.0657i)|01101> + (0.0487-0.0125i)|01110> + (0.0064-0.1043i)|01111> + (0.3541-0.0103i)|10000> + (0.0525+0.0427i)|10001> + (0.1451-0.2184i)|10010> + (-0.0102-0.0433i)|10011> + (-0.1290+0.0015i)|10100> + (0.0202-0.0149i)|10101> + (-0.0765+0.1230i)|10110> + (-0.1569+0.1666i)|10111> + (0.0992+0.1020i)|11000> + (-0.0130-0.0138i)|11001> + (0.0810+0.0158i)|11010> + (-0.0196+0.0110i)|11011> + (0.0435+0.0270i)|11100> + (-0.0017-0.0176i)|11101> + (0.0589+0.0061i)|11110> + (-0.0615-0.0144i)|11111>\n  |00111> -> (-0.0392-0.1330i)|00000> + (0.0657+0.0723i)|00001> + (0.1873-0.4975i)|00010> + (0.0496+0.1078i)|00011> + (-0.0187+0.0405i)|00100> + (0.2137+0.2369i)|00101> + (-0.0420+0.1042i)|00110> + (0.4086-0.0984i)|00111> + (0.0431-0.0542i)|01000> + (0.0049-0.0291i)|01001> + (0.1199-0.0933i)|01010> + (0.0043-0.0392i)|01011> + (0.0081-0.0195i)|01100> + (-0.0229+0.0984i)|01101> + (0.0308-0.0178i)|01110> + (0.1202+0.0347i)|01111> + (0.3333-0.2267i)|10000> + (0.0333+0.0202i)|10001> + (0.0797+0.1250i)|10010> + (0.0458-0.0311i)|10011> + (-0.0173+0.2709i)|10100> + (0.0017+0.0799i)|10101> + (-0.0097+0.0490i)|10110> + (-0.1088+0.0369i)|10111> + (0.1404-0.0073i)|11000> + (-0.0117-0.0159i)|11001> + (0.0061+0.0730i)|11010> + (-0.0107-0.0080i)|11011> + (0.0607-0.0805i)|11100> + (0.0033+0.0343i)|11101> + (0.0223-0.0020i)|11110> + (-0.0366+0.0033i)|11111>\n  |01000> -> (-0.0293-0.0936i)|00000> + (-0.0316+0.0200i)|00001> + (-0.0785-0.0701i)|00010> + (0.0357-0.0574i)|00011> + (0.0092+0.0321i)|00100> + (-0.0097+0.0613i)|00101> + (0.0803-0.0197i)|00110> + (0.0335-0.0987i)|00111> + (-0.1141+0.2369i)|01000> + (-0.0827-0.0628i)|01001> + (0.1495+0.3537i)|01010> + (0.1998-0.1097i)|01011> + (-0.0692+0.0689i)|01100> + (0.1960-0.0345i)|01101> + (0.2761+0.0679i)|01110> + (-0.2471+0.2438i)|01111> + (-0.0614-0.1440i)|10000> + (0.0307+0.0317i)|10001> + (0.0582+0.0805i)|10010> + (-0.0172+0.0138i)|10011> + (0.0172-0.0012i)|10100> + (0.0550-0.0450i)|10101> + (-0.0432+0.0033i)|10110> + (-0.0045+0.0506i)|10111> + (-0.0356+0.4158i)|11000> + (0.0201+0.1394i)|11001> + (0.0229-0.2733i)|11010> + (-0.0631+0.0247i)|11011> + (0.0592+0.0270i)|11100> + (-0.2220-0.0091i)|11101> + (-0.1151-0.0586i)|11110> + (0.1120-0.1325i)|11111>\n  |01001> -> (-0.0611-0.1064i)|00000> + (0.0691-0.0029i)|00010> + (-0.0187-0.0547i)|00011> + (0.0962+0.0113i)|00100> + (0.0569-0.0302i)|00101> + (-0.0336+0.0389i)|00110> + (-0.0784-0.0218i)|00111> + (-0.2057+0.4148i)|01000> + (0.0164+0.0404i)|01001> + (-0.1421-0.0429i)|01010> + (0.0413-0.1686i)|01011> + (0.1351+0.3031i)|01100> + (-0.1497-0.1494i)|01101> + (-0.1477+0.0492i)|01110> + (0.1809+0.1411i)|01111> + (0.1171-0.0220i)|10000> + (-0.0331+0.0018i)|10001> + (0.0377+0.1332i)|10010> + (0.0061-0.0203i)|10011> + (-0.0277+0.0221i)|10100> + (-0.0853-0.0139i)|10101> + (-0.0150-0.0040i)|10110> + (0.0359-0.0744i)|10111> + (-0.2157-0.1457i)|11000> + (-0.0738-0.0543i)|11001> + (0.2670-0.3102i)|11010> + (0.0771+0.0067i)|11011> + (-0.0660-0.0461i)|11100> + (0.1663+0.2035i)|11101> + (-0.0057-0.0684i)|11110> + (-0.2666+0.0462i)|11111>\n  |01010> -> (-0.0424+0.0648i)|00000> + (-0.0870+0.0410i)|00001> + (0.0445-0.0646i)|00010> + (0.0183+0.0050i)|00011> + (-0.0051-0.0117i)|00100> + (-0.0597+0.1034i)|00101> + (-0.0133+0.0319i)|00110> + (0.0533-0.0418i)|00111> + (0.2397+0.0509i)|01000> + (-0.2753-0.1853i)|01001> + (-0.2473+0.0361i)|01010> + (0.0309+0.0383i)|01011> + (0.0407-0.0352i)|01100> + (0.4538-0.0297i)|01101> + (-0.0884+0.0483i)|01110> + (-0.1722-0.0590i)|01111> + (0.0712-0.0144i)|10000> + (0.0114-0.0370i)|10001> + (0.0176-0.1136i)|10010> + (0.0130+0.0165i)|10011> + (0.0136+0.0251i)|10100> + (-0.0788-0.0944i)|10101> + (-0.0130+0.0251i)|10110> + (0.1229-0.1007i)|10111> + (-0.2029-0.1201i)|11000> + (0.0851-0.0046i)|11001> + (-0.2653+0.0950i)|11010> + (-0.0267+0.0558i)|11011> + (-0.0179+0.0760i)|11100> + (-0.0209+0.2719i)|11101> + (-0.0753-0.0093i)|11110> + (-0.3934-0.1433i)|11111>\n  |01011> -> (-0.0530+0.0197i)|00000> + (-0.0136+0.0284i)|00001> + (0.0751+0.0798i)|00010> + (0.0536+0.0178i)|00011> + (0.0201-0.0267i)|00100> + (0.0912+0.0579i)|00101> + (-0.0195-0.0242i)|00110> + (0.0421-0.1016i)|00111> + (0.1113+0.1452i)|01000> + (-0.0925+0.0019i)|01001> + (-0.0374-0.3809i)|01010> + (0.1543+0.1425i)|01011> + (0.0897+0.0354i)|01100> + (-0.0599-0.2878i)|01101> + (-0.0308-0.1197i)|01110> + (-0.3574+0.2152i)|01111> + (0.0707+0.0259i)|10000> + (0.0180+0.0070i)|10001> + (0.0787-0.0330i)|10010> + (-0.0535-0.0309i)|10011> + (-0.0490-0.0097i)|10100> + (0.1342+0.0629i)|10101> + (0.0136+0.0436i)|10110> + (-0.1152-0.0376i)|10111> + (-0.1109-0.2018i)|11000> + (0.0404+0.0578i)|11001> + (-0.1355-0.0927i)|11010> + (-0.0512-0.1619i)|11011> + (-0.1009-0.1158i)|11100> + (-0.2455-0.3119i)|11101> + (-0.0566+0.1070i)|11110> + (0.0993+0.2434i)|11111>\n  |01100> -> (0.0899+0.0440i)|00000> + (-0.0565-0.0102i)|00001> + (-0.0458+0.0246i)|00010> + (-0.0330-0.0802i)|00011> + (0.1442-0.0657i)|00100> + (-0.0204+0.0733i)|00110> + (0.0568+0.0131i)|00111> + (-0.0241-0.3326i)|01000> + (-0.0121-0.1467i)|01001> + (0.1695+0.0149i)|01010> + (0.0882-0.2966i)|01011> + (0.3902+0.2815i)|01100> + (0.0167-0.0125i)|01101> + (-0.2567+0.1735i)|01110> + (-0.1216-0.1344i)|01111> + (-0.0228+0.0005i)|10000> + (-0.0029+0.0993i)|10001> + (0.0005+0.0109i)|10010> + (-0.0827+0.0032i)|10011> + (-0.0135-0.0494i)|10100> + (0.0007-0.0353i)|10101> + (0.1243+0.0421i)|10110> + (0.0211+0.0024i)|10111> + (0.0047+0.0740i)|11000> + (-0.1821+0.2396i)|11001> + (-0.1004-0.1381i)|11011> + (0.0469-0.2235i)|11100> + (-0.0603+0.0783i)|11101> + (0.0986+0.2911i)|11110> + (0.0063-0.0560i)|11111>\n  |01101> -> (-0.0168+0.0267i)|00000> + (-0.0321+0.0262i)|00001> + (0.0852+0.0076i)|00010> + (-0.0428-0.1105i)|00011> + (-0.0614+0.0630i)|00100> + (-0.0011-0.0355i)|00101> + (0.0935-0.0999i)|00110> + (0.0431+0.0540i)|00111> + (0.1104+0.0050i)|01000> + (-0.0672-0.0450i)|01001> + (-0.2424-0.1576i)|01010> + (0.0699-0.3773i)|01011> + (-0.3331+0.0099i)|01100> + (-0.0861+0.0356i)|01101> + (0.4136-0.1400i)|01110> + (-0.0339-0.2291i)|01111> + (-0.0007-0.0165i)|10000> + (0.0395+0.0888i)|10001> + (-0.0363-0.0056i)|10010> + (-0.1501-0.0400i)|10100> + (-0.0471+0.0032i)|10101> + (-0.0000+0.0398i)|10110> + (-0.0027-0.0178i)|10111> + (-0.0353+0.0213i)|11000> + (-0.0478+0.2791i)|11001> + (0.0940+0.0717i)|11010> + (0.0345+0.0398i)|11011> + (-0.2424-0.2751i)|11100> + (0.1271+0.0752i)|11101> + (-0.1141+0.1401i)|11110> + (0.0021+0.0534i)|11111>\n  |01110> -> (-0.0281+0.0145i)|00000> + (0.0904+0.0129i)|00001> + (-0.0086+0.0282i)|00010> + (-0.0813-0.0958i)|00011> + (-0.0219+0.0302i)|00100> + (0.0025+0.0278i)|00101> + (-0.0510+0.0887i)|00110> + (0.0516-0.0276i)|00111> + (0.0581+0.0656i)|01000> + (0.2078+0.2655i)|01001> + (0.0551-0.0869i)|01010> + (-0.0894-0.3440i)|01011> + (-0.0766-0.0475i)|01100> + (0.0853-0.0550i)|01101> + (-0.2319+0.1387i)|01110> + (-0.2014+0.0226i)|01111> + (0.0382+0.0353i)|10000> + (0.0674+0.1386i)|10001> + (-0.0078-0.0467i)|10010> + (0.0757-0.0658i)|10011> + (0.0859+0.0405i)|10100> + (-0.0113-0.0189i)|10101> + (-0.0984-0.0072i)|10110> + (-0.0427+0.0412i)|10111> + (-0.0286-0.1559i)|11000> + (-0.0440+0.3605i)|11001> + (-0.0870+0.1082i)|11010> + (0.3301+0.0938i)|11011> + (0.1338+0.2428i)|11100> + (-0.0213+0.0537i)|11101> + (-0.1329-0.2861i)|11110> + (0.1787+0.0002i)|11111>\n  |01111> -> (0.0961-0.1240i)|00001> + (0.0272-0.0160i)|00010> + (0.0231-0.0190i)|00011> + (-0.0196-0.0576i)|00100> + (-0.0019+0.0995i)|00101> + (0.0516-0.0207i)|00110> + (0.0094-0.0060i)|00111> + (0.0161-0.0152i)|01000> + (0.4756+0.0737i)|01001> + (-0.0837-0.0095i)|01010> + (0.0418+0.0722i)|01011> + (0.1185-0.0908i)|01100> + (0.2918-0.1628i)|01101> + (0.1047+0.0608i)|01110> + (-0.0250+0.0112i)|01111> + (-0.0166-0.0288i)|10000> + (-0.0420-0.0268i)|10001> + (0.0322-0.0005i)|10010> + (0.1383-0.0958i)|10011> + (-0.0950+0.0285i)|10100> + (-0.0134-0.0227i)|10101> + (0.1301-0.0009i)|10110> + (0.0100+0.0232i)|10111> + (-0.0110+0.0908i)|11000> + (-0.0943-0.2071i)|11001> + (-0.0408-0.0843i)|11010> + (0.4182+0.1649i)|11011> + (-0.2877-0.0911i)|11100> + (-0.0611+0.0457i)|11101> + (0.1839+0.3046i)|11110> + (0.0383-0.0638i)|11111>\n  |10000> -> (0.0789-0.0119i)|00000> + (0.3835+0.2347i)|00001> + (-0.0119+0.0037i)|00010> + (-0.1751+0.1920i)|00011> + (0.0892-0.1321i)|00100> + (-0.0710-0.0732i)|00101> + (-0.2730+0.1190i)|00110> + (0.0515-0.0049i)|00111> + (0.0046+0.0159i)|01000> + (0.0021-0.1490i)|01001> + (0.0506-0.0088i)|01011> + (-0.0381-0.0135i)|01100> + (0.0026-0.0349i)|01101> + (0.0696+0.0128i)|01110> + (0.0084+0.0244i)|01111> + (-0.1469-0.0888i)|10000> + (-0.1474+0.1485i)|10001> + (0.1151-0.1317i)|10010> + (-0.2842-0.2977i)|10011> + (-0.2060+0.1226i)|10100> + (-0.0341-0.0887i)|10101> + (-0.0710-0.2791i)|10110> + (0.2656-0.0116i)|10111> + (-0.0211-0.0592i)|11000> + (0.0446-0.0202i)|11001> + (0.0629+0.0067i)|11010> + (-0.0230+0.1614i)|11011> + (0.0841+0.0159i)|11100> + (0.0017-0.0365i)|11101> + (-0.0679+0.0984i)|11110> + (0.0568+0.0805i)|11111>\n  |10001> -> (-0.0548-0.0163i)|00000> + (-0.2186+0.2162i)|00001> + (0.1011+0.0942i)|00010> + (0.1495+0.3391i)|00011> + (-0.1723+0.0913i)|00100> + (-0.0988-0.0937i)|00101> + (0.2185-0.2552i)|00110> + (-0.0080-0.1019i)|00111> + (-0.0016-0.0180i)|01000> + (0.0824-0.0080i)|01001> + (0.0091+0.0371i)|01010> + (0.0004-0.1134i)|01011> + (0.0326+0.0284i)|01100> + (-0.0099-0.0506i)|01101> + (-0.0887+0.0361i)|01110> + (0.0090-0.0264i)|01111> + (0.0540-0.0029i)|10000> + (-0.0240+0.4290i)|10001> + (-0.0430+0.0316i)|10010> + (-0.0536-0.2578i)|10011> + (0.2624+0.1010i)|10100> + (-0.1897-0.2279i)|10101> + (-0.0566+0.1617i)|10110> + (0.0402+0.0760i)|10111> + (0.0129+0.0104i)|11000> + (0.1036-0.1423i)|11001> + (-0.0266-0.0022i)|11010> + (-0.0411+0.0672i)|11011> + (-0.0491-0.0936i)|11100> + (-0.0187-0.1105i)|11101> + (0.0489-0.0360i)|11110> + (-0.0079+0.0294i)|11111>\n  |10010> -> (-0.1506-0.0390i)|00000> + (-0.1255+0.1210i)|00001> + (0.0245+0.0973i)|00010> + (0.3089+0.0402i)|00011> + (-0.3133-0.0889i)|00100> + (-0.0067-0.0528i)|00101> + (0.0904+0.3378i)|00110> + (-0.0734+0.1185i)|00111> + (-0.0345-0.0433i)|01000> + (0.0328+0.0196i)|01001> + (-0.0190+0.0287i)|01010> + (-0.0775-0.0709i)|01011> + (0.0471+0.0727i)|01100> + (0.0136-0.0083i)|01101> + (0.0330-0.1186i)|01110> + (-0.0422+0.0102i)|01111> + (-0.2785-0.0812i)|10000> + (0.2972-0.0107i)|10001> + (0.0458+0.1269i)|10010> + (0.1042-0.1285i)|10011> + (-0.3598+0.2056i)|10100> + (0.0081+0.0361i)|10101> + (0.2488-0.0892i)|10110> + (-0.0866+0.0948i)|10111> + (-0.0772-0.0801i)|11000> + (-0.0860-0.0681i)|11001> + (-0.0354+0.0389i)|11010> + (-0.0499-0.0236i)|11011> + (0.1716+0.0102i)|11100> + (-0.0066+0.0093i)|11101> + (-0.0539-0.0540i)|11110> + (-0.0519-0.0140i)|11111>\n  |10011> -> (-0.0016+0.0833i)|00000> + (-0.1989+0.0170i)|00001> + (-0.0769-0.0830i)|00010> + (0.2409-0.0654i)|00011> + (0.4393-0.0675i)|00100> + (0.0649-0.0699i)|00101> + (-0.2044+0.0107i)|00110> + (-0.0201+0.1032i)|00111> + (-0.0215+0.0198i)|01000> + (0.0233+0.0453i)|01001> + (0.0101-0.0427i)|01010> + (-0.0665-0.0435i)|01011> + (-0.0941-0.1151i)|01100> + (0.0177+0.0079i)|01101> + (0.0329+0.0508i)|01110> + (-0.0329+0.0194i)|01111> + (-0.0349+0.0891i)|10000> + (0.1801+0.1045i)|10001> + (-0.2050-0.1751i)|10010> + (0.3099-0.0291i)|10011> + (-0.0150+0.2265i)|10100> + (-0.1634-0.0145i)|10101> + (-0.3797-0.1867i)|10110> + (0.0066+0.1671i)|10111> + (-0.0268+0.0248i)|11000> + (-0.0203-0.0738i)|11001> + (0.0176-0.1000i)|11010> + (-0.0705-0.1036i)|11011> + (0.0244-0.0501i)|11100> + (-0.0434-0.0437i)|11101> + (0.0175+0.1649i)|11110> + (-0.0547+0.0324i)|11111>\n  |10100> -> (0.0669-0.0143i)|00000> + (-0.0990-0.1030i)|00001> + (0.0225+0.3714i)|00010> + (0.0922-0.0705i)|00011> + (0.0249-0.0228i)|00100> + (-0.2867+0.2039i)|00101> + (-0.1438-0.0066i)|00110> + (0.3402-0.2623i)|00111> + (0.0025+0.0578i)|01001> + (-0.0553+0.1018i)|01010> + (-0.0314+0.0053i)|01011> + (-0.0132-0.0060i)|01100> + (-0.1257-0.0432i)|01101> + (0.0331+0.0252i)|01110> + (0.1268-0.0202i)|01111> + (-0.1038-0.3152i)|10000> + (-0.0899-0.2795i)|10001> + (0.0509-0.0230i)|10010> + (-0.0172+0.0642i)|10011> + (0.0280+0.0642i)|10100> + (-0.3469-0.1931i)|10101> + (-0.0095-0.0330i)|10110> + (-0.1211+0.0898i)|10111> + (0.0372-0.1180i)|11000> + (-0.0215+0.1062i)|11001> + (0.0204-0.0155i)|11011> + (0.0037-0.0229i)|11100> + (-0.0777-0.1089i)|11101> + (-0.0117+0.0185i)|11110> + (-0.0429+0.0099i)|11111>\n  |10101> -> (0.0544-0.0077i)|00000> + (0.0410-0.1032i)|00001> + (0.3510+0.0151i)|00010> + (0.0433+0.0682i)|00011> + (-0.0264+0.0652i)|00100> + (0.2052-0.4362i)|00101> + (-0.0411+0.0260i)|00110> + (0.2614+0.2443i)|00111> + (-0.0075+0.0083i)|01000> + (-0.0300+0.0116i)|01001> + (0.0929+0.0751i)|01010> + (0.0110-0.0383i)|01011> + (0.0126+0.0044i)|01100> + (0.1376-0.0154i)|01101> + (0.0261+0.0010i)|01110> + (0.0310+0.1271i)|01111> + (-0.2340-0.1535i)|10000> + (-0.0155-0.0835i)|10001> + (0.1525-0.1549i)|10010> + (0.2466+0.0779i)|10011> + (0.1586-0.0750i)|10100> + (-0.1200+0.0271i)|10101> + (0.0467+0.1617i)|10110> + (0.2774-0.1814i)|10111> + (-0.0354-0.0955i)|11000> + (-0.0126+0.0357i)|11001> + (0.0682+0.0359i)|11010> + (-0.0217-0.0908i)|11011> + (-0.0626-0.0147i)|11100> + (-0.0387-0.0489i)|11101> + (0.0395-0.0437i)|11110> + (0.0892+0.0568i)|11111>\n  |10110> -> (0.4700-0.1191i)|00000> + (-0.0743+0.0346i)|00001> + (0.0733+0.0797i)|00010> + (0.0325-0.0839i)|00011> + (0.0138+0.0956i)|00100> + (-0.0185+0.0451i)|00101> + (-0.1022+0.0207i)|00110> + (-0.1233-0.0199i)|00111> + (0.0992+0.0997i)|01000> + (0.0097+0.0109i)|01001> + (0.0014+0.0631i)|01010> + (-0.0328+0.0108i)|01011> + (0.0166-0.0208i)|01100> + (0.0324+0.0299i)|01110> + (-0.0116-0.0450i)|01111> + (-0.1197-0.0439i)|10000> + (0.1456+0.0892i)|10001> + (0.4465-0.1022i)|10010> + (0.0159-0.1751i)|10011> + (0.0671+0.0490i)|10100> + (0.2803+0.0072i)|10101> + (-0.2370+0.1360i)|10110> + (-0.3561-0.1269i)|10111> + (0.0002-0.0562i)|11000> + (-0.0215-0.0604i)|11001> + (0.1150+0.1155i)|11010> + (-0.0602+0.0270i)|11011> + (-0.0132-0.0341i)|11100> + (0.0823+0.0627i)|11101> + (0.0880+0.0501i)|11110> + (-0.0306-0.1398i)|11111>\n  |10111> -> (0.1662-0.3042i)|00000> + (-0.0019+0.0342i)|00001> + (-0.2362+0.1795i)|00010> + (0.0830-0.0917i)|00011> + (-0.0692+0.1425i)|00100> + (0.0164-0.0641i)|00101> + (0.0845-0.0274i)|00110> + (-0.1403-0.1107i)|00111> + (0.1303-0.0167i)|01000> + (0.0126-0.0047i)|01001> + (-0.0709+0.0181i)|01010> + (-0.0354-0.0001i)|01011> + (0.0559-0.0237i)|01100> + (0.0100+0.0145i)|01101> + (-0.0192-0.0139i)|01110> + (-0.0114-0.0317i)|01111> + (0.3987+0.0117i)|10000> + (-0.0484-0.0243i)|10001> + (0.0637-0.3177i)|10010> + (0.1381-0.0389i)|10011> + (-0.2060+0.2023i)|10100> + (-0.2315+0.2436i)|10101> + (0.1301+0.0593i)|10110> + (0.2404-0.1837i)|10111> + (0.1203+0.0617i)|11000> + (0.0088+0.0149i)|11001> + (0.1022-0.0650i)|11010> + (-0.0437-0.0408i)|11011> + (0.1040-0.0292i)|11100> + (-0.1194+0.0211i)|11101> + (-0.0086-0.0570i)|11110> + (0.1144+0.0281i)|11111>\n  |11000> -> (0.0881-0.0778i)|00000> + (0.0184+0.0418i)|00001> + (0.0656+0.0619i)|00010> + (-0.0296+0.0253i)|00011> + (-0.0179+0.0360i)|00100> + (0.0438+0.0482i)|00101> + (-0.0629-0.0161i)|00110> + (0.0001+0.0514i)|00111> + (-0.2600-0.0641i)|01000> + (-0.0648+0.1437i)|01001> + (-0.0487-0.3386i)|01010> + (-0.1287+0.0138i)|01011> + (-0.1267-0.0052i)|01100> + (0.0090-0.2038i)|01101> + (-0.1468-0.1557i)|01110> + (0.1598-0.1521i)|01111> + (0.0066-0.1852i)|10000> + (-0.0234+0.0448i)|10001> + (0.0823-0.0723i)|10010> + (0.0040+0.0134i)|10011> + (0.0260-0.0075i)|10100> + (0.0281+0.0790i)|10101> + (-0.0024+0.0109i)|10110> + (0.1211+0.0324i)|10111> + (-0.2850+0.4585i)|11000> + (-0.0943+0.0601i)|11001> + (-0.2360-0.0460i)|11010> + (-0.0124+0.0088i)|11011> + (0.0840+0.0432i)|11100> + (0.0268-0.2032i)|11101> + (0.0109+0.0059i)|11110> + (-0.1087-0.2857i)|11111>\n  |11001> -> (0.0204+0.0900i)|00000> + (0.0183-0.0015i)|00001> + (0.0228+0.1115i)|00010> + (0.0221-0.0105i)|00011> + (-0.0582-0.0393i)|00100> + (-0.0209-0.0834i)|00101> + (-0.0372-0.0108i)|00110> + (0.0343-0.0642i)|00111> + (0.2715-0.2181i)|01000> + (0.0351+0.0396i)|01001> + (0.1603-0.2534i)|01010> + (0.0802+0.0439i)|01011> + (0.0363-0.2314i)|01100> + (-0.1593+0.2315i)|01101> + (-0.0681-0.1053i)|01110> + (-0.1974+0.0375i)|01111> + (-0.0572-0.0820i)|10000> + (0.0128-0.0045i)|10001> + (-0.0035+0.1628i)|10010> + (0.0206-0.0563i)|10011> + (0.0261+0.0351i)|10100> + (0.0306-0.0760i)|10101> + (-0.0336+0.0104i)|10110> + (0.0598-0.1220i)|10111> + (-0.0597+0.2581i)|11000> + (0.0385-0.0000i)|11001> + (0.3978-0.1936i)|11010> + (0.1450-0.0331i)|11011> + (-0.0343+0.1403i)|11100> + (-0.1356+0.1250i)|11101> + (-0.0526-0.0593i)|11110> + (-0.3557+0.0194i)|11111>\n  |11010> -> (0.0455+0.0582i)|00000> + (0.0722+0.0004i)|00001> + (0.0233-0.0825i)|00010> + (0.0437-0.0222i)|00011> + (-0.0040-0.0179i)|00100> + (0.0703-0.0651i)|00101> + (0.0318+0.0123i)|00110> + (0.1005-0.0665i)|00111> + (0.0334-0.2486i)|01000> + (0.1028+0.2136i)|01001> + (-0.1433+0.1564i)|01010> + (0.1580-0.0063i)|01011> + (0.0316-0.0390i)|01100> + (-0.3332-0.1286i)|01101> + (0.0953+0.0693i)|01110> + (-0.3022-0.0008i)|01111> + (-0.0073+0.0948i)|10000> + (-0.0338-0.0155i)|10001> + (0.1099-0.0090i)|10010> + (-0.0140+0.0274i)|10011> + (-0.0101-0.0154i)|10100> + (-0.0431+0.0866i)|10101> + (-0.0555+0.0079i)|10110> + (0.1396+0.0319i)|10111> + (0.1227-0.1830i)|11000> + (-0.0314-0.1268i)|11001> + (-0.1999-0.2754i)|11010> + (-0.1004+0.0355i)|11011> + (-0.0084-0.0515i)|11100> + (0.2496-0.0657i)|11101> + (-0.1253-0.1073i)|11110> + (-0.1117-0.4139i)|11111>\n  |11011> -> (-0.0208+0.0681i)|00000> + (-0.0337+0.0139i)|00001> + (0.0447-0.0477i)|00010> + (-0.0220-0.0651i)|00011> + (-0.0370-0.0287i)|00100> + (-0.0104+0.1099i)|00101> + (-0.0288+0.0390i)|00110> + (-0.1012+0.0014i)|00111> + (0.1997-0.0981i)|01000> + (-0.0763-0.0831i)|01001> + (-0.1985+0.1129i)|01010> + (0.0343-0.2190i)|01011> + (-0.0112-0.1563i)|01100> + (0.2096-0.1219i)|01101> + (-0.1368+0.0728i)|01110> + (0.3186+0.1493i)|01111> + (-0.0491+0.0606i)|10000> + (0.0332+0.0186i)|10001> + (-0.0316+0.0890i)|10010> + (0.0186+0.0149i)|10011> + (-0.0080-0.0477i)|10100> + (0.1225+0.1452i)|10101> + (-0.0022-0.0262i)|10110> + (0.0693+0.0017i)|10111> + (0.1698-0.0816i)|11000> + (0.0423+0.1147i)|11001> + (0.2564-0.1090i)|11010> + (0.0247+0.0945i)|11011> + (0.0333-0.1027i)|11100> + (-0.0946-0.5406i)|11101> + (0.0601-0.0745i)|11110> + (-0.1611-0.1283i)|11111>\n  |11100> -> (-0.0401-0.0593i)|00000> + (0.0379+0.0852i)|00001> + (-0.0269-0.0111i)|00010> + (-0.0170+0.0041i)|00011> + (-0.1037-0.0238i)|00100> + (-0.0192+0.0071i)|00101> + (0.0166+0.0497i)|00110> + (0.0007+0.0167i)|00111> + (-0.1187+0.1971i)|01000> + (-0.1535+0.2792i)|01001> + (0.0430+0.0987i)|01010> + (0.0360-0.0064i)|01011> + (-0.0592-0.2963i)|01100> + (0.0516+0.0397i)|01101> + (-0.1290+0.0922i)|01110> + (0.0630-0.0435i)|01111> + (-0.0027+0.0427i)|10000> + (-0.0397+0.0480i)|10001> + (-0.0344+0.0276i)|10010> + (-0.1296-0.0757i)|10011> + (-0.0108+0.0927i)|10100> + (0.0928+0.1704i)|10110> + (0.0544+0.0299i)|10111> + (0.1155-0.0966i)|11000> + (-0.1062+0.0409i)|11001> + (0.0968+0.0314i)|11010> + (-0.0321-0.4072i)|11011> + (-0.2077+0.2356i)|11100> + (0.0059-0.0103i)|11101> + (-0.2443+0.4471i)|11110> + (-0.0167-0.1562i)|11111>\n  |11101> -> (-0.0273+0.0131i)|00000> + (0.0720+0.0272i)|00001> + (-0.0501-0.0424i)|00010> + (-0.0366+0.0472i)|00011> + (-0.0497-0.0190i)|00100> + (-0.0468+0.0018i)|00101> + (-0.0969-0.0172i)|00110> + (-0.0073-0.0390i)|00111> + (0.0940+0.0735i)|01000> + (0.0707+0.2649i)|01001> + (0.0663+0.1951i)|01010> + (-0.1085+0.0782i)|01011> + (-0.1571-0.1340i)|01100> + (0.1113+0.1208i)|01101> + (-0.1978-0.1596i)|01110> + (-0.0422+0.1141i)|01111> + (0.0231-0.0323i)|10000> + (-0.0169+0.0528i)|10001> + (-0.1018-0.0616i)|10011> + (-0.1358-0.1707i)|10100> + (-0.0258-0.0405i)|10101> + (-0.0275-0.1016i)|10110> + (-0.1019+0.0155i)|11000> + (-0.0880+0.0547i)|11001> + (-0.0586-0.0048i)|11010> + (-0.0182-0.3529i)|11011> + (-0.0474-0.5621i)|11100> + (0.0021+0.1025i)|11101> + (0.2344-0.2338i)|11110> + (-0.0382-0.0279i)|11111>\n  |11110> -> (0.0294+0.0377i)|00000> + (0.0206+0.0472i)|00001> + (0.0480-0.0201i)|00010> + (0.0159+0.1246i)|00011> + (0.0780-0.0186i)|00100> + (-0.0102+0.0248i)|00101> + (0.0715-0.0692i)|00110> + (-0.0678-0.0217i)|00111> + (0.0311-0.1589i)|01000> + (0.0112+0.2105i)|01001> + (-0.1679-0.0152i)|01010> + (-0.1721+0.3643i)|01011> + (0.2134+0.1726i)|01100> + (0.1086+0.0017i)|01101> + (0.3406-0.0743i)|01110> + (0.1561+0.1650i)|01111> + (-0.0084+0.0457i)|10000> + (-0.0450+0.2125i)|10001> + (-0.0103+0.0130i)|10010> + (0.0094+0.0111i)|10011> + (0.0371+0.0425i)|10100> + (0.0076-0.0458i)|10101> + (-0.0468-0.0132i)|10110> + (0.0147-0.0076i)|10111> + (0.0626-0.0787i)|11000> + (-0.4024+0.3900i)|11001> + (0.0661-0.0208i)|11010> + (-0.0476-0.0268i)|11011> + (0.0217+0.1036i)|11100> + (-0.1002+0.0757i)|11101> + (-0.0683-0.0672i)|11110> + (-0.0824-0.0158i)|11111>\n  |11111> -> (-0.0167+0.0152i)|00000> + (-0.1025+0.0340i)|00001> + (-0.0306-0.0127i)|00010> + (0.0445+0.0839i)|00011> + (-0.0621+0.0659i)|00100> + (0.0352-0.0643i)|00101> + (-0.0296+0.0738i)|00110> + (-0.0133-0.0433i)|00111> + (0.0673+0.0190i)|01000> + (-0.2075-0.2164i)|01001> + (0.0964+0.0888i)|01010> + (-0.1097+0.3386i)|01011> + (-0.3144-0.0368i)|01100> + (-0.2316-0.0112i)|01101> + (-0.2716+0.1521i)|01110> + (-0.0305+0.1623i)|01111> + (0.0251+0.0922i)|10001> + (0.0494+0.0269i)|10010> + (0.1630+0.0081i)|10011> + (-0.0559-0.0302i)|10100> + (-0.0358+0.0093i)|10101> + (0.1022+0.0460i)|10110> + (-0.0064+0.0360i)|10111> + (0.0043-0.0218i)|11000> + (-0.0969+0.3044i)|11001> + (-0.0395-0.1496i)|11010> + (0.1955+0.3310i)|11011> + (-0.0521-0.1038i)|11100> + (0.1194+0.0711i)|11101> + (0.0604+0.2468i)|11110> + (0.0707-0.0637i)|11111>\n\nIdentify the bug and write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "A 2-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\ns q[0];\nry(6.233205422191898) q[1];\nh q[0];\nt q[1];\nrz(2.6377277960320695) q[1];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |00>: 0.4997\n  |01>: 0.4997\n  |10>: 0.0003\n  |11>: 0.0003\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |00>: 0.4802\n  |01>: 0.4802\n  |10>: 0.0198\n  |11>: 0.0198\n\nTotal variation distance between expected and observed: 0.0389\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "A 2-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\ncz q[0],q[1];\ncx q[0],q[1];\nx q[0];\ns q[0];\nz q[0];\ncz q[1],q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |00>: 1.0000\n  |01>: 0.0000\n  |10>: 0.0000\n  |11>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |00>: 0.0709\n  |01>: 0.8532\n  |10>: 0.0379\n  |11>: 0.0379\n\nTotal variation distance between expected and observed: 0.9291\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "A 2-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\ns q[0];\nx q[1];\ncx q[1],q[0];\ncx q[0],q[1];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |01>: 1.0000\n  |00>: 0.0000\n  |10>: 0.0000\n  |11>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |01>: 0.8984\n  |00>: 0.0377\n  |10>: 0.0377\n  |11>: 0.0261\n\nTotal variation distance between expected and observed: 0.1016\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "A 2-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nt q[0];\nry(3.546845264651369) q[0];\nt q[1];\nx q[0];\ncz q[1],q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |10>: 0.9595\n  |11>: 0.0405\n  |00>: 0.0000\n  |01>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |10>: 0.0250\n  |11>: 0.0143\n  |00>: 0.8761\n  |01>: 0.0846\n\nTotal variation distance between expected and observed: 0.9607\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "A 2-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nx q[0];\ns q[0];\nz q[0];\nrx(4.0640737710208565) q[1];\nrz(3.2013648199070324) q[1];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |11>: 0.8019\n  |01>: 0.1981\n  |00>: 0.0000\n  |10>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |11>: 0.7554\n  |01>: 0.2056\n  |00>: 0.0083\n  |10>: 0.0306\n\nTotal variation distance between expected and observed: 0.0465\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nh q[0];\ny q[2];\nz q[0];\nry(4.595429162898796) q[0];\nh q[0];\nry(1.1297748410442046) q[2];\nrz(3.6364650998332704) q[1];\nrx(3.478600366653917) q[2];\nh q[2];\ncz q[2],q[0];\nz q[2];\ncx q[2],q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |101>: 0.5316\n  |100>: 0.4205\n  |000>: 0.0267\n  |001>: 0.0211\n  |010>: 0.0000\n  |110>: 0.0000\n  |111>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |101>: 0.4627\n  |100>: 0.3799\n  |000>: 0.0769\n  |001>: 0.0672\n  |010>: 0.0010\n  |110>: 0.0051\n  |111>: 0.0063\n\nTotal variation distance between expected and observed: 0.1096\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncz q[0],q[2];\ncx q[1],q[0];\ny q[0];\ncz q[2],q[1];\nx q[2];\nh q[1];\ns q[1];\nt q[2];\ncx q[2],q[1];\ncx q[1],q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |100>: 0.5000\n  |111>: 0.5000\n  |000>: 0.0000\n  |001>: 0.0000\n  |010>: 0.0000\n  |011>: 0.0000\n  |101>: 0.0000\n  |110>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |100>: 0.0346\n  |111>: 0.0346\n  |000>: 0.0089\n  |001>: 0.0401\n  |010>: 0.0401\n  |011>: 0.0089\n  |101>: 0.4163\n  |110>: 0.4163\n\nTotal variation distance between expected and observed: 0.9308\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ny q[1];\ncz q[1],q[2];\nz q[0];\nh q[1];\ncz q[2],q[0];\ns q[0];\nh q[2];\nh q[1];\ncx q[2],q[1];\nx q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |011>: 0.5000\n  |101>: 0.5000\n  |001>: 0.0000\n  |111>: 0.0000\n  |000>: 0.0000\n  |010>: 0.0000\n  |100>: 0.0000\n  |110>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |011>: 0.4276\n  |101>: 0.4276\n  |001>: 0.0406\n  |111>: 0.0406\n  |000>: 0.0028\n  |010>: 0.0290\n  |100>: 0.0290\n  |110>: 0.0028\n\nTotal variation distance between expected and observed: 0.1448\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nry(4.90345463572115) q[1];\nry(3.96557427988722) q[2];\nz q[1];\ncx q[0],q[2];\nry(5.216146853823407) q[1];\nry(0.7938516107442662) q[0];\nz q[0];\nrx(0.2199799637049444) q[2];\nt q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |100>: 0.3860\n  |110>: 0.3212\n  |000>: 0.0782\n  |101>: 0.0678\n  |010>: 0.0651\n  |111>: 0.0564\n  |001>: 0.0137\n  |011>: 0.0114\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |100>: 0.6080\n  |110>: 0.0397\n  |000>: 0.1486\n  |101>: 0.1404\n  |010>: 0.0097\n  |111>: 0.0092\n  |001>: 0.0417\n  |011>: 0.0027\n\nTotal variation distance between expected and observed: 0.3929\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncx q[2],q[0];\ns q[2];\nh q[1];\nrz(3.549070927955319) q[1];\nz q[2];\nz q[2];\nh q[0];\nz q[1];\ncx q[1],q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |000>: 0.2500\n  |001>: 0.2500\n  |010>: 0.2500\n  |011>: 0.2500\n  |100>: 0.0000\n  |101>: 0.0000\n  |110>: 0.0000\n  |111>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |000>: 0.2341\n  |001>: 0.2341\n  |010>: 0.2341\n  |011>: 0.2341\n  |100>: 0.0159\n  |101>: 0.0159\n  |110>: 0.0159\n  |111>: 0.0159\n\nTotal variation distance between expected and observed: 0.0635\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ny q[1];\nry(0.6942173114049845) q[0];\ncx q[0],q[2];\nry(6.138627849323446) q[2];\ny q[1];\nh q[2];\nrx(1.4605216698306211) q[1];\nx q[0];\ns q[0];\nx q[2];\nx q[1];\ny q[0];\nx q[0];\ny q[1];\nh q[1];\ncz q[1],q[2];\nry(3.1416378329493813) q[0];\ncz q[1],q[0];\nx q[0];\nx q[1];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |001>: 0.2529\n  |011>: 0.2529\n  |111>: 0.1892\n  |101>: 0.1892\n  |100>: 0.0331\n  |110>: 0.0331\n  |010>: 0.0248\n  |000>: 0.0248\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |001>: 0.2194\n  |011>: 0.2194\n  |111>: 0.1731\n  |101>: 0.1731\n  |100>: 0.0546\n  |110>: 0.0546\n  |010>: 0.0529\n  |000>: 0.0529\n\nTotal variation distance between expected and observed: 0.0993\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ny q[0];\nz q[0];\nrx(2.9023731792410192) q[1];\nry(5.200616505001642) q[1];\ncz q[0],q[2];\ncz q[2],q[0];\ny q[2];\ncx q[2],q[0];\ns q[1];\nh q[0];\nt q[0];\ns q[0];\ncz q[2],q[1];\ncx q[2],q[1];\ncz q[1],q[0];\nrz(1.4461854753991825) q[0];\nh q[1];\ncx q[0],q[2];\ns q[0];\ns q[1];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |100>: 0.3383\n  |011>: 0.3383\n  |110>: 0.1617\n  |001>: 0.1617\n  |000>: 0.0000\n  |010>: 0.0000\n  |101>: 0.0000\n  |111>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |100>: 0.1738\n  |011>: 0.1738\n  |110>: 0.2467\n  |001>: 0.2467\n  |000>: 0.0437\n  |010>: 0.0358\n  |101>: 0.0358\n  |111>: 0.0437\n\nTotal variation distance between expected and observed: 0.3290\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nrz(5.587598069145495) q[0];\nx q[2];\nry(3.321340432892243) q[0];\nry(5.745489147881786) q[2];\nz q[0];\nh q[2];\ny q[2];\ncx q[2],q[0];\nrz(1.1310788047604496) q[1];\ncz q[1],q[0];\nt q[1];\nt q[1];\ny q[1];\ns q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |110>: 0.7500\n  |011>: 0.2420\n  |111>: 0.0061\n  |010>: 0.0020\n  |000>: 0.0000\n  |001>: 0.0000\n  |100>: 0.0000\n  |101>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |110>: 0.6058\n  |011>: 0.2320\n  |111>: 0.0578\n  |010>: 0.0292\n  |000>: 0.0051\n  |001>: 0.0161\n  |100>: 0.0418\n  |101>: 0.0122\n\nTotal variation distance between expected and observed: 0.1541\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nrx(4.390097046656369) q[1];\nt q[0];\nx q[2];\nz q[1];\nt q[1];\nrx(-0.45032746271864055) q[1];\nh q[1];\nh q[0];\nz q[0];\nx q[1];\ncz q[2],q[1];\ncx q[2],q[0];\ncz q[1],q[0];\nry(3.2460947028273317) q[2];\nt q[2];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |010>: 0.4165\n  |011>: 0.4165\n  |000>: 0.0821\n  |001>: 0.0821\n  |110>: 0.0011\n  |111>: 0.0011\n  |100>: 0.0002\n  |101>: 0.0002\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |010>: 0.3471\n  |011>: 0.3471\n  |000>: 0.1084\n  |001>: 0.1084\n  |110>: 0.0307\n  |111>: 0.0307\n  |100>: 0.0138\n  |101>: 0.0138\n\nTotal variation distance between expected and observed: 0.1389\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "A 3-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nx q[1];\ny q[1];\ns q[2];\ncx q[0],q[2];\nh q[2];\ny q[0];\nrz(4.858823513094322) q[0];\ns q[1];\ncz q[2],q[1];\ncz q[0],q[1];\ncx q[1],q[0];\nry(0.3407620959327636) q[2];\ns q[2];\nz q[1];\ns q[0];\nrz(4.42487483309752) q[0];\nt q[0];\nry(2.9662692166428033) q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |100>: 0.6620\n  |000>: 0.3303\n  |101>: 0.0051\n  |001>: 0.0026\n  |010>: 0.0000\n  |011>: 0.0000\n  |110>: 0.0000\n  |111>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |100>: 0.4922\n  |000>: 0.2760\n  |101>: 0.0687\n  |001>: 0.0438\n  |010>: 0.0166\n  |011>: 0.0396\n  |110>: 0.0252\n  |111>: 0.0378\n\nTotal variation distance between expected and observed: 0.2241\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[2],q[3];\nh q[1];\nh q[3];\ncx q[0],q[1];\nry(2.573998407719185) q[0];\ncx q[1],q[3];\nh q[2];\nrx(3.034716258920142) q[0];\ny q[0];\nt q[3];\ncx q[0],q[3];\ncx q[3],q[2];\ns q[3];\ns q[1];\nrx(5.850554537252634) q[2];\ny q[1];\ncz q[2],q[1];\nt q[3];\ncx q[2],q[1];\nry(4.413235888303129) q[2];\ns q[0];\nt q[2];\nrx(4.106199854534486) q[0];\nx q[3];\ncz q[0],q[3];\nt q[1];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |1000>: 0.1151\n  |1010>: 0.1151\n  |1100>: 0.1151\n  |1110>: 0.1151\n  |0000>: 0.1086\n  |0010>: 0.1086\n  |0100>: 0.1086\n  |0110>: 0.1086\n  |0001>: 0.0164\n  |0011>: 0.0164\n  |0101>: 0.0164\n  |0111>: 0.0164\n  |1001>: 0.0099\n  |1011>: 0.0099\n  |1101>: 0.0099\n  |1111>: 0.0099\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |1000>: 0.0987\n  |1010>: 0.0987\n  |1100>: 0.0987\n  |1110>: 0.0987\n  |0000>: 0.0951\n  |0010>: 0.0951\n  |0100>: 0.0951\n  |0110>: 0.0951\n  |0001>: 0.0299\n  |0011>: 0.0299\n  |0101>: 0.0299\n  |0111>: 0.0299\n  |1001>: 0.0263\n  |1011>: 0.0263\n  |1101>: 0.0263\n  |1111>: 0.0263\n\nTotal variation distance between expected and observed: 0.1197\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncz q[3],q[0];\nt q[2];\nx q[2];\nx q[1];\ncx q[1],q[3];\ny q[0];\nrz(6.209467891514083) q[2];\ny q[1];\ncx q[2],q[0];\ncx q[3],q[2];\ns q[2];\nrz(-0.30949016254557676) q[1];\nrz(4.738918429570839) q[3];\ns q[2];\ncx q[3],q[2];\nh q[1];\nx q[3];\nh q[0];\ncz q[1],q[0];\nrz(5.317205769319798) q[0];\ns q[0];\nz q[2];\nz q[1];\nry(1.9822852908305795) q[2];\ncx q[3],q[0];\ns q[0];\nrx(3.1100395202504285) q[1];\nry(5.866421744799235) q[2];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |0101>: 0.1257\n  |0111>: 0.1257\n  |0100>: 0.1257\n  |0110>: 0.1257\n  |0001>: 0.1243\n  |0011>: 0.1243\n  |0000>: 0.1243\n  |0010>: 0.1243\n  |1000>: 0.0000\n  |1001>: 0.0000\n  |1010>: 0.0000\n  |1011>: 0.0000\n  |1100>: 0.0000\n  |1101>: 0.0000\n  |1110>: 0.0000\n  |1111>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |0101>: 0.1067\n  |0111>: 0.1067\n  |0100>: 0.1067\n  |0110>: 0.1067\n  |0001>: 0.1059\n  |0011>: 0.1059\n  |0000>: 0.1059\n  |0010>: 0.1059\n  |1000>: 0.0186\n  |1001>: 0.0186\n  |1010>: 0.0186\n  |1011>: 0.0186\n  |1100>: 0.0187\n  |1101>: 0.0187\n  |1110>: 0.0187\n  |1111>: 0.0187\n\nTotal variation distance between expected and observed: 0.1495\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nrz(5.00772352073245) q[1];\ncz q[3],q[0];\ncz q[3],q[2];\nrz(2.6504435221787856) q[2];\nx q[1];\ns q[1];\nt q[1];\nt q[1];\ncz q[2],q[1];\ncx q[1],q[2];\nt q[3];\ny q[3];\ncz q[1],q[0];\ncx q[1],q[0];\ncx q[0],q[3];\nrx(4.721215303440683) q[1];\ncz q[1],q[2];\nh q[1];\ncx q[0],q[3];\nt q[0];\nh q[1];\nh q[1];\ny q[2];\nrx(4.823603865410804) q[3];\nry(2.898938342120762) q[0];\ny q[2];\nrx(3.0138447352437527) q[2];\ncz q[0],q[1];\ns q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |1000>: 0.2726\n  |1010>: 0.2726\n  |0000>: 0.2181\n  |0010>: 0.2181\n  |1001>: 0.0041\n  |1011>: 0.0041\n  |0001>: 0.0032\n  |0011>: 0.0032\n  |1100>: 0.0011\n  |1110>: 0.0011\n  |0100>: 0.0009\n  |0110>: 0.0009\n  |1101>: 0.0000\n  |1111>: 0.0000\n  |0101>: 0.0000\n  |0111>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |1000>: 0.1764\n  |1010>: 0.1764\n  |0000>: 0.1473\n  |0010>: 0.1473\n  |1001>: 0.0438\n  |1011>: 0.0438\n  |0001>: 0.0387\n  |0011>: 0.0387\n  |1100>: 0.0281\n  |1110>: 0.0281\n  |0100>: 0.0243\n  |0110>: 0.0243\n  |1101>: 0.0224\n  |1111>: 0.0224\n  |0101>: 0.0191\n  |0111>: 0.0191\n\nTotal variation distance between expected and observed: 0.3339\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nx q[0];\ncz q[3],q[0];\nry(2.488215421766685) q[3];\ncz q[2],q[3];\nt q[0];\nh q[0];\nh q[1];\ns q[2];\ny q[1];\nt q[3];\ny q[3];\nrz(4.994394377350793) q[2];\ncx q[3],q[1];\nt q[3];\nry(3.9497983066763553) q[2];\ncz q[1],q[3];\nh q[2];\nrx(2.0026062018409263) q[3];\ncz q[2],q[1];\ncz q[2],q[0];\ncz q[2],q[0];\nry(2.922629114558955) q[0];\ny q[1];\ncz q[1],q[3];\ncx q[1],q[2];\nh q[2];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |1000>: 0.1944\n  |1110>: 0.1944\n  |1001>: 0.1250\n  |1111>: 0.1250\n  |0000>: 0.0974\n  |0110>: 0.0974\n  |0001>: 0.0626\n  |0111>: 0.0626\n  |1100>: 0.0083\n  |1010>: 0.0083\n  |1101>: 0.0054\n  |1011>: 0.0054\n  |0010>: 0.0042\n  |0100>: 0.0042\n  |0011>: 0.0027\n  |0101>: 0.0027\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |1000>: 0.1281\n  |1110>: 0.1281\n  |1001>: 0.0903\n  |1111>: 0.0903\n  |0000>: 0.0802\n  |0110>: 0.0802\n  |0001>: 0.0571\n  |0111>: 0.0571\n  |1100>: 0.0500\n  |1010>: 0.0500\n  |1101>: 0.0368\n  |1011>: 0.0368\n  |0010>: 0.0331\n  |0100>: 0.0331\n  |0011>: 0.0245\n  |0101>: 0.0245\n\nTotal variation distance between expected and observed: 0.2475\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nrz(2.797128645370943) q[0];\ny q[2];\nz q[0];\nrx(6.27418513273209) q[2];\ncz q[3],q[1];\ncz q[3],q[1];\ncz q[2],q[1];\ns q[3];\nrz(0.4882728695007828) q[1];\nh q[0];\nx q[3];\ncx q[3],q[0];\nt q[3];\nz q[1];\ncx q[3],q[1];\nrx(1.6628796327401585) q[2];\ns q[1];\nz q[1];\nh q[2];\nry(1.3165151979730891) q[1];\ncx q[1],q[3];\ny q[1];\ny q[0];\nz q[3];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |0000>: 0.1564\n  |0001>: 0.1564\n  |0100>: 0.1564\n  |0101>: 0.1564\n  |1010>: 0.0936\n  |1011>: 0.0936\n  |1110>: 0.0936\n  |1111>: 0.0936\n  |0010>: 0.0000\n  |0011>: 0.0000\n  |0110>: 0.0000\n  |0111>: 0.0000\n  |1000>: 0.0000\n  |1001>: 0.0000\n  |1100>: 0.0000\n  |1101>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |0000>: 0.1230\n  |0001>: 0.1230\n  |0100>: 0.1230\n  |0101>: 0.1230\n  |1010>: 0.0850\n  |1011>: 0.0850\n  |1110>: 0.0850\n  |1111>: 0.0850\n  |0010>: 0.0223\n  |0011>: 0.0223\n  |0110>: 0.0223\n  |0111>: 0.0223\n  |1000>: 0.0197\n  |1001>: 0.0197\n  |1100>: 0.0197\n  |1101>: 0.0197\n\nTotal variation distance between expected and observed: 0.1679\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nrz(5.6653520449477615) q[2];\ncz q[3],q[1];\nz q[0];\ncz q[3],q[1];\nx q[1];\ncz q[3],q[1];\ncx q[3],q[0];\nh q[0];\ncx q[1],q[2];\nx q[1];\ncx q[1],q[2];\nx q[1];\ncz q[1],q[3];\ncx q[0],q[2];\nx q[1];\ncx q[1],q[0];\ncx q[3],q[2];\ncz q[1],q[2];\nx q[1];\ncz q[2],q[3];\ncz q[1],q[2];\ny q[0];\ncx q[3],q[1];\ny q[1];\nrx(2.4254829344000775) q[0];\ncz q[2],q[1];\nry(6.019153586587893) q[1];\nx q[2];\nry(1.3331731288912216) q[1];\nrx(5.244222112794835) q[2];\nrz(0.681303639896158) q[1];\ncz q[3],q[2];\ncx q[1],q[0];\nx q[2];\ncx q[2],q[3];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |0000>: 0.2190\n  |1101>: 0.2190\n  |0001>: 0.1512\n  |1100>: 0.1512\n  |0011>: 0.0768\n  |1110>: 0.0768\n  |0010>: 0.0530\n  |1111>: 0.0530\n  |0100>: 0.0000\n  |0101>: 0.0000\n  |0110>: 0.0000\n  |0111>: 0.0000\n  |1000>: 0.0000\n  |1001>: 0.0000\n  |1010>: 0.0000\n  |1011>: 0.0000\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |0000>: 0.1292\n  |1101>: 0.1292\n  |0001>: 0.1107\n  |1100>: 0.1107\n  |0011>: 0.0835\n  |1110>: 0.0835\n  |0010>: 0.0711\n  |1111>: 0.0711\n  |0100>: 0.0253\n  |0101>: 0.0263\n  |0110>: 0.0289\n  |0111>: 0.0250\n  |1000>: 0.0263\n  |1001>: 0.0253\n  |1010>: 0.0250\n  |1011>: 0.0289\n\nTotal variation distance between expected and observed: 0.2607\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ns q[2];\nh q[2];\nz q[2];\ny q[3];\nh q[0];\ns q[2];\ncx q[3],q[2];\nh q[2];\ns q[3];\nx q[3];\nz q[1];\ny q[2];\nx q[1];\nx q[0];\ncz q[2],q[0];\nh q[1];\ncx q[2],q[1];\ny q[3];\ny q[2];\nt q[2];\nrx(3.7254565401449025) q[3];\ny q[0];\ns q[1];\ncz q[2],q[1];\ncz q[0],q[2];\ns q[2];\ncz q[2],q[1];\ns q[1];\ns q[2];\nrx(3.677722170724191) q[2];\nz q[2];\nh q[3];\ncz q[1],q[2];\ncx q[0],q[2];\nh q[2];\nrx(1.111203710156386) q[0];\ncx q[1],q[0];\nz q[2];\ncx q[0],q[2];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |0000>: 0.1067\n  |0011>: 0.1067\n  |1000>: 0.1067\n  |1011>: 0.1067\n  |1101>: 0.1067\n  |1110>: 0.1067\n  |0101>: 0.1067\n  |0110>: 0.1067\n  |0010>: 0.0183\n  |1001>: 0.0183\n  |1010>: 0.0183\n  |1100>: 0.0183\n  |1111>: 0.0183\n  |0001>: 0.0183\n  |0111>: 0.0183\n  |0100>: 0.0183\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |0000>: 0.0778\n  |0011>: 0.0778\n  |1000>: 0.0778\n  |1011>: 0.0778\n  |1101>: 0.0778\n  |1110>: 0.0778\n  |0101>: 0.0778\n  |0110>: 0.0778\n  |0010>: 0.0472\n  |1001>: 0.0472\n  |1010>: 0.0472\n  |1100>: 0.0472\n  |1111>: 0.0472\n  |0001>: 0.0472\n  |0111>: 0.0472\n  |0100>: 0.0472\n\nTotal variation distance between expected and observed: 0.2313\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[1],q[0];\nt q[2];\nt q[1];\ny q[1];\nrz(3.9324037458554004) q[2];\ns q[0];\nh q[3];\nz q[3];\nrz(1.5603198875015798) q[2];\ncx q[3],q[2];\nh q[0];\ns q[0];\ns q[2];\ny q[2];\ncz q[2],q[1];\nry(5.207891885759399) q[1];\nz q[2];\ncz q[2],q[0];\ns q[0];\ncz q[0],q[1];\nh q[1];\nry(0.7201056383962905) q[3];\ncz q[1],q[0];\nz q[1];\ny q[1];\nrz(1.2973644995545521) q[2];\nry(2.349329069797054) q[0];\nry(0.8172389899267917) q[0];\nrx(6.106233100598071) q[0];\nry(2.778195862064673) q[2];\nt q[1];\ns q[3];\ns q[0];\nz q[3];\nt q[3];\nrz(4.791095437018639) q[2];\nrz(5.530003485445102) q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |0011>: 0.2264\n  |1111>: 0.2239\n  |0000>: 0.1738\n  |1100>: 0.1713\n  |1000>: 0.0608\n  |0100>: 0.0605\n  |1101>: 0.0167\n  |0001>: 0.0142\n  |1110>: 0.0137\n  |0010>: 0.0113\n  |1011>: 0.0082\n  |0111>: 0.0079\n  |0110>: 0.0044\n  |1010>: 0.0042\n  |0101>: 0.0015\n  |1001>: 0.0012\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |0011>: 0.1463\n  |1111>: 0.1453\n  |0000>: 0.1231\n  |1100>: 0.1220\n  |1000>: 0.0654\n  |0100>: 0.0652\n  |1101>: 0.0438\n  |0001>: 0.0428\n  |1110>: 0.0438\n  |0010>: 0.0427\n  |1011>: 0.0422\n  |0111>: 0.0419\n  |0110>: 0.0190\n  |1010>: 0.0188\n  |0101>: 0.0190\n  |1001>: 0.0188\n\nTotal variation distance between expected and observed: 0.2588\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nrz(2.441160786815985) q[2];\nrx(2.947217229918511) q[3];\ny q[2];\ns q[1];\nrz(4.334434171142473) q[2];\nrz(4.177097469236492) q[3];\nt q[1];\nt q[1];\ncx q[3],q[1];\nz q[0];\nz q[2];\nx q[0];\nrx(2.951727016556071) q[0];\nry(0.5646865487388301) q[3];\ncx q[0],q[3];\ncz q[2],q[3];\ncz q[3],q[0];\ny q[2];\ncz q[2],q[3];\ny q[0];\nh q[1];\ncz q[3],q[1];\ncz q[2],q[3];\ncz q[0],q[2];\nry(0.42172113258774646) q[2];\nx q[3];\nry(2.2118029583969134) q[3];\nrx(3.696321875949893) q[3];\nrx(4.542022582014654) q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |0000>: 0.2239\n  |0010>: 0.2028\n  |0001>: 0.1758\n  |1011>: 0.1372\n  |1010>: 0.0717\n  |0011>: 0.0665\n  |1000>: 0.0505\n  |1001>: 0.0279\n  |0100>: 0.0103\n  |0110>: 0.0093\n  |0101>: 0.0081\n  |1111>: 0.0063\n  |1110>: 0.0033\n  |0111>: 0.0030\n  |1100>: 0.0023\n  |1101>: 0.0013\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |0000>: 0.1671\n  |0010>: 0.1161\n  |0001>: 0.1231\n  |1011>: 0.0736\n  |1010>: 0.1124\n  |0011>: 0.1037\n  |1000>: 0.0613\n  |1001>: 0.0542\n  |0100>: 0.0317\n  |0110>: 0.0294\n  |0101>: 0.0241\n  |1111>: 0.0177\n  |1110>: 0.0230\n  |0111>: 0.0242\n  |1100>: 0.0207\n  |1101>: 0.0178\n\nTotal variation distance between expected and observed: 0.2597\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T5", "task_code": "B3_noise_logic", "task_name": "Noise Discrimination", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "A 4-qubit circuit was run on noisy hardware. Determine whether the output deviation is from a LOGIC BUG in the circuit or from HARDWARE NOISE ONLY.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nry(1.379715152317794) q[3];\nx q[1];\ny q[2];\nrz(3.5329643872532563) q[2];\nrx(0.7347007796089802) q[3];\ns q[1];\ncz q[3],q[0];\nx q[2];\nt q[3];\ns q[1];\ncx q[1],q[0];\nt q[2];\nrz(4.169045552872129) q[1];\nry(4.832641044318824) q[1];\ncz q[2],q[1];\ncz q[2],q[0];\ncz q[1],q[0];\nrz(0.9747333972815793) q[0];\nt q[1];\ncz q[1],q[0];\nry(5.260220794806753) q[2];\ns q[1];\ny q[0];\nrx(4.1552607964370845) q[0];\nrx(1.8245673927876904) q[1];\ny q[0];\nx q[1];\ncz q[1],q[2];\nh q[1];\nry(3.0339362042338553) q[2];\ny q[1];\ncz q[3],q[0];\ncx q[3],q[0];\n```\n\nNoise model (depolarizing, applied after each gate):\n  After each 1-qubit gate: p = 0.02 (D(\u03c1) = (1-p)\u03c1 + p/3\u00b7(X\u03c1X + Y\u03c1Y + Z\u03c1Z))\n  After each 2-qubit gate: p = 0.05 (D(\u03c1) = (1-p)\u03c1 + p/15\u00b7\u03a3_{P\u2260II} P\u03c1P)\n\nExpected noiseless output (from the INTENDED correct circuit):\n  |0100>: 0.2885\n  |1101>: 0.2172\n  |0101>: 0.0889\n  |0010>: 0.0817\n  |1100>: 0.0670\n  |1011>: 0.0615\n  |0110>: 0.0566\n  |1111>: 0.0426\n  |0011>: 0.0252\n  |1010>: 0.0190\n  |0111>: 0.0175\n  |1110>: 0.0131\n  |0000>: 0.0092\n  |1001>: 0.0070\n  |0001>: 0.0028\n  |1000>: 0.0021\n\nObserved noisy output (from running THIS circuit on noisy hardware):\n  |0100>: 0.1806\n  |1101>: 0.1432\n  |0101>: 0.0869\n  |0010>: 0.0675\n  |1100>: 0.0711\n  |1011>: 0.0536\n  |0110>: 0.0757\n  |1111>: 0.0602\n  |0011>: 0.0356\n  |1010>: 0.0290\n  |0111>: 0.0474\n  |1110>: 0.0385\n  |0000>: 0.0381\n  |1001>: 0.0303\n  |0001>: 0.0234\n  |1000>: 0.0190\n\nTotal variation distance between expected and observed: 0.2060\n\nIMPORTANT: The noise model above would cause a TVD of roughly 0.02\u20130.05 per gate on a typical circuit. Simulate this circuit with the given noise model to decide.\n\nIf there IS a logic bug: identify it, write a Qiskit function `solve()` that returns the CORRECTED QuantumCircuit.\nIf there is NO logic bug (noise only): write `solve()` that returns the ORIGINAL circuit UNCHANGED.\n\nOnly return the code for `solve()`. No explanation.\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "Analyze the following 2-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nh q[0];\ncx q[0],q[1];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "Analyze the following 3-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nh q[0];\ncx q[0],q[1];\ncx q[1],q[2];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "Analyze the following 2-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nh q[0];\ncx q[0],q[1];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "Analyze the following 2-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nh q[0];\ncx q[0],q[1];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "Analyze the following 2-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[2];\nh q[0];\ncx q[0],q[1];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "Analyze the following 3-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nh q[0];\ncx q[0],q[1];\ncx q[1],q[2];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "Analyze the following 4-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nswap q[1],q[2];\nswap q[0],q[3];\nh q[3];\ncp(-pi/2) q[3],q[2];\nh q[2];\ncp(-pi/4) q[3],q[1];\ncp(-pi/2) q[2],q[1];\nh q[1];\ncp(-pi/8) q[3],q[0];\ncp(-pi/4) q[2],q[0];\ncp(-pi/2) q[1],q[0];\nh q[0];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "Analyze the following 3-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nswap q[0],q[2];\nh q[2];\ncp(-pi/2) q[2],q[1];\nh q[1];\ncp(-pi/4) q[2],q[0];\ncp(-pi/2) q[1],q[0];\nh q[0];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "Analyze the following 4-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nswap q[1],q[2];\nswap q[0],q[3];\nh q[3];\ncp(-pi/2) q[3],q[2];\nh q[2];\ncp(-pi/4) q[3],q[1];\ncp(-pi/2) q[2],q[1];\nh q[1];\ncp(-pi/8) q[3],q[0];\ncp(-pi/4) q[2],q[0];\ncp(-pi/2) q[1],q[0];\nh q[0];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "Analyze the following 3-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nh q[0];\ncp(pi/2) q[1],q[0];\ncp(pi/4) q[2],q[0];\nh q[1];\ncp(pi/2) q[2],q[1];\nh q[2];\nswap q[0],q[2];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "Analyze the following 4-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nu2(0,pi) q[0];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[3];\ncx q[1],q[3];\nu2(0,pi) q[1];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "Analyze the following 4-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nu2(0,pi) q[0];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[3];\ncx q[1],q[3];\nu2(0,pi) q[1];\ncx q[2],q[3];\nu2(0,pi) q[2];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "Analyze the following 5-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\nu2(0,pi) q[0];\nu3(0,0,pi/4) q[1];\ncx q[1],q[0];\nu3(0,0,-pi/4) q[0];\ncx q[1],q[0];\nu3(0,0,pi/4) q[0];\nu2(0,pi) q[1];\nu3(0,0,pi/8) q[2];\ncx q[2],q[0];\nu3(0,0,-pi/8) q[0];\ncx q[2],q[0];\nu3(0,0,pi/8) q[0];\nu3(0,0,pi/4) q[2];\ncx q[2],q[1];\nu3(0,0,-pi/4) q[1];\ncx q[2],q[1];\nu3(0,0,pi/4) q[1];\nu2(0,pi) q[2];\nu3(0,0,pi/16) q[3];\ncx q[3],q[0];\nu3(0,0,-pi/16) q[0];\ncx q[3],q[0];\nu3(0,0,pi/16) q[0];\nu3(0,0,pi/8) q[3];\ncx q[3],q[1];\nu3(0,0,-pi/8) q[1];\ncx q[3],q[1];\nu3(0,0,pi/8) q[1];\nu3(0,0,pi/4) q[3];\ncx q[3],q[2];\nu3(0,0,-pi/4) q[2];\ncx q[3],q[2];\nu3(0,0,pi/4) q[2];\nu2(0,pi) q[3];\nu3(0,0,pi/32) q[4];\ncx q[4],q[0];\nu3(0,0,-pi/32) q[0];\ncx q[4],q[0];\nu3(0,0,pi/32) q[0];\nu3(0,0,pi/16) q[4];\ncx q[4],q[1];\nu3(0,0,-pi/16) q[1];\ncx q[4],q[1];\nu3(0,0,pi/16) q[1];\nu3(0,0,pi/8) q[4];\ncx q[4],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[4],q[2];\nu3(0,0,pi/8) q[2];\nu3(0,0,pi/4) q[4];\ncx q[4],q[3];\nu3(0,0,-pi/4) q[3];\ncx q[4],q[3];\nu3(0,0,pi/4) q[3];\ncx q[1],q[3];\ncx q[3],q[1];\ncx q[1],q[3];\nu2(0,pi) q[4];\ncx q[0],q[4];\ncx q[4],q[0];\ncx q[0],q[4];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "Analyze the following 3-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nu2(0,pi) q[0];\nu3(0,0,pi/4) q[1];\ncx q[1],q[0];\nu3(0,0,-pi/4) q[0];\ncx q[1],q[0];\nu3(0,0,pi/4) q[0];\nu2(0,pi) q[1];\nu3(0,0,pi/8) q[2];\ncx q[2],q[0];\nu3(0,0,-pi/8) q[0];\ncx q[2],q[0];\nu3(0,0,pi/8) q[0];\nu3(0,0,pi/4) q[2];\ncx q[2],q[1];\nu3(0,0,-pi/4) q[1];\ncx q[2],q[1];\nu3(0,0,pi/4) q[1];\nu2(0,pi) q[2];\ncx q[0],q[2];\ncx q[2],q[0];\ncx q[0],q[2];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "Analyze the following 3-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\nu2(0,pi) q[0];\ncx q[2],q[1];\nu2(0,pi) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/4) q[2];\ncx q[0],q[2];\nu3(0,0,pi/4) q[2];\ncx q[1],q[2];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[2];\ncx q[0],q[2];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu2(0,pi) q[0];\nu3(0,0,pi/4) q[2];\nu2(0,pi) q[2];\ncx q[2],q[1];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "Analyze the following 4-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[3];\ncx q[0],q[3];\nu2(0,pi) q[0];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "Analyze the following 6-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nu2(0,pi) q[0];\nu3(pi,0,pi) q[0];\nu3(0,0,pi/8) q[0];\nu2(0,pi) q[1];\nu3(pi,0,pi) q[1];\nu3(0,0,pi/8) q[1];\ncx q[0],q[1];\nu3(0,0,-pi/8) q[1];\ncx q[0],q[1];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[2];\nu3(0,0,pi/8) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu3(0,0,pi/8) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu2(0,pi) q[3];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[4];\nu3(pi,0,pi) q[4];\nu2(0,pi) q[5];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\nu2(0,pi) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[1];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,pi/8) q[2];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[0];\ncx q[0],q[1];\nu3(0,0,-pi/8) q[1];\ncx q[0],q[1];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu3(0,0,pi/8) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu2(0,pi) q[5];\nu3(0,0,-pi/4) q[5];\nu2(0,pi) q[5];\ncx q[4],q[5];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\nu3(0,0,pi/4) q[5];\ncx q[4],q[5];\nu3(0,0,pi/4) q[4];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu2(0,pi) q[5];\nu3(0,0,-pi/4) q[5];\nu2(0,pi) q[5];\ncx q[4],q[5];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\nu3(0,0,pi/4) q[5];\ncx q[4],q[5];\nu3(0,0,pi/4) q[4];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[3],q[4];\nu2(0,pi) q[4];\ncx q[1],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\nu3(0,0,pi/4) q[4];\ncx q[1],q[4];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,-pi/8) q[4];\nu2(0,pi) q[4];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\ncx q[2],q[3];\nu3(0,0,pi/4) q[2];\nu3(0,0,-pi/4) q[3];\ncx q[2],q[3];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,pi/8) q[4];\nu2(0,pi) q[4];\ncx q[1],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\nu3(0,0,pi/4) q[4];\ncx q[1],q[4];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,-pi/8) q[4];\nu2(0,pi) q[4];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\ncx q[2],q[3];\nu3(0,0,pi/4) q[2];\nu3(0,0,-pi/4) q[3];\ncx q[2],q[3];\nu2(0,pi) q[3];\ncx q[1],q[3];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\nu3(0,0,pi/4) q[3];\ncx q[1],q[3];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[3];\nu2(0,pi) q[3];\nu3(0,0,-pi/16) q[3];\ncx q[2],q[3];\nu3(0,0,pi/16) q[3];\nu2(0,pi) q[3];\ncx q[1],q[3];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\nu3(0,0,pi/4) q[3];\ncx q[1],q[3];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[3];\nu2(0,pi) q[3];\nu3(0,0,-pi/16) q[3];\ncx q[2],q[3];\ncx q[0],q[2];\nu3(0,0,-pi/32) q[2];\ncx q[1],q[2];\nu3(0,0,pi/32) q[2];\ncx q[0],q[2];\nu3(0,0,-pi/32) q[2];\ncx q[1],q[2];\nu3(0,0,pi/32) q[1];\ncx q[0],q[1];\nu3(0,0,-pi/32) q[1];\ncx q[0],q[1];\nu3(0,0,pi/32) q[0];\nu3(pi,0,pi) q[0];\nu2(0,pi) q[0];\nu3(pi,0,pi) q[1];\nu2(0,pi) q[1];\nu3(0,0,pi/32) q[2];\nu3(pi,0,pi) q[2];\nu2(0,pi) q[2];\nu3(0,0,pi/16) q[3];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[3];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,pi/8) q[4];\nu3(pi,0,pi) q[4];\nu2(0,pi) q[4];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu2(0,pi) q[5];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "Analyze the following 6-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nu2(0,pi) q[0];\nu3(pi,0,pi) q[0];\nu3(0,0,pi/8) q[0];\nu2(0,pi) q[1];\nu3(pi,0,pi) q[1];\nu3(0,0,pi/8) q[1];\ncx q[0],q[1];\nu3(0,0,-pi/8) q[1];\ncx q[0],q[1];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[2];\nu3(0,0,pi/8) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu3(0,0,pi/8) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu2(0,pi) q[3];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[4];\nu3(pi,0,pi) q[4];\nu2(0,pi) q[5];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\nu2(0,pi) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[1];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,pi/8) q[2];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[0];\ncx q[0],q[1];\nu3(0,0,-pi/8) q[1];\ncx q[0],q[1];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu3(0,0,pi/8) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/8) q[2];\ncx q[0],q[2];\nu2(0,pi) q[5];\nu3(0,0,-pi/4) q[5];\nu2(0,pi) q[5];\ncx q[4],q[5];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\nu3(0,0,pi/4) q[5];\ncx q[4],q[5];\nu3(0,0,pi/4) q[4];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu2(0,pi) q[5];\nu3(0,0,-pi/4) q[5];\nu2(0,pi) q[5];\ncx q[4],q[5];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\nu3(0,0,pi/4) q[5];\ncx q[4],q[5];\nu3(0,0,pi/4) q[4];\nu3(0,0,-pi/4) q[5];\ncx q[3],q[5];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[3],q[4];\nu2(0,pi) q[4];\ncx q[1],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\nu3(0,0,pi/4) q[4];\ncx q[1],q[4];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,-pi/8) q[4];\nu2(0,pi) q[4];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\ncx q[2],q[3];\nu3(0,0,pi/4) q[2];\nu3(0,0,-pi/4) q[3];\ncx q[2],q[3];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,pi/8) q[4];\nu2(0,pi) q[4];\ncx q[1],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\nu3(0,0,pi/4) q[4];\ncx q[1],q[4];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[4];\ncx q[0],q[4];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,-pi/8) q[4];\nu2(0,pi) q[4];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[2],q[4];\ncx q[2],q[3];\nu3(0,0,pi/4) q[2];\nu3(0,0,-pi/4) q[3];\ncx q[2],q[3];\nu2(0,pi) q[3];\ncx q[1],q[3];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\nu3(0,0,pi/4) q[3];\ncx q[1],q[3];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[3];\nu2(0,pi) q[3];\nu3(0,0,-pi/16) q[3];\ncx q[2],q[3];\nu3(0,0,pi/16) q[3];\nu2(0,pi) q[3];\ncx q[1],q[3];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\nu3(0,0,pi/4) q[3];\ncx q[1],q[3];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[3];\ncx q[0],q[3];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\nu3(0,0,pi/4) q[3];\nu2(0,pi) q[3];\nu3(0,0,-pi/16) q[3];\ncx q[2],q[3];\ncx q[0],q[2];\nu3(0,0,-pi/32) q[2];\ncx q[1],q[2];\nu3(0,0,pi/32) q[2];\ncx q[0],q[2];\nu3(0,0,-pi/32) q[2];\ncx q[1],q[2];\nu3(0,0,pi/32) q[1];\ncx q[0],q[1];\nu3(0,0,-pi/32) q[1];\ncx q[0],q[1];\nu3(0,0,pi/32) q[0];\nu3(pi,0,pi) q[0];\nu2(0,pi) q[0];\nu3(pi,0,pi) q[1];\nu2(0,pi) q[1];\nu3(0,0,pi/32) q[2];\nu3(pi,0,pi) q[2];\nu2(0,pi) q[2];\nu3(0,0,pi/16) q[3];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[3];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\nu3(0,0,pi/8) q[4];\nu3(pi,0,pi) q[4];\nu2(0,pi) q[4];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/4) q[5];\nu2(0,pi) q[5];\nu2(0,pi) q[5];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "Analyze the following 4-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nu2(0,pi) q[0];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[3];\nu3(pi,0,pi) q[3];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "Analyze the following 6-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nu2(0,pi) q[0];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu2(0,pi) q[2];\nu2(0,pi) q[3];\nu2(0,pi) q[3];\nu2(0,pi) q[4];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\ncx q[4],q[5];\nu2(0,pi) q[4];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "Analyze the following 7-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\nu2(0,pi) q[0];\nu3(pi,0,pi) q[0];\nu2(0,pi) q[1];\nu3(pi,0,pi) q[1];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[2];\nu2(0,pi) q[3];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[4];\nu3(pi,0,pi) q[4];\nu2(0,pi) q[4];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\nu2(0,pi) q[5];\nu3(pi,0,pi) q[5];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\ncx q[5],q[3];\nu3(0,0,-pi/4) q[3];\nu3(0,0,pi/4) q[5];\ncx q[5],q[3];\ncx q[5],q[3];\nu3(pi,0,pi) q[5];\nu3(pi,0,pi) q[5];\ncx q[5],q[3];\ncx q[5],q[4];\nu2(0,pi) q[4];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu2(0,pi) q[5];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\ncx q[5],q[3];\nu3(0,0,-pi/4) q[3];\nu3(0,0,pi/4) q[5];\ncx q[5],q[3];\ncx q[5],q[3];\nu3(pi,0,pi) q[5];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu2(0,pi) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/4) q[2];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\ncx q[0],q[2];\nu3(0,0,pi/4) q[2];\ncx q[1],q[2];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[2];\ncx q[0],q[2];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\ncx q[0],q[1];\nu3(pi,0,pi) q[0];\nu3(pi,0,pi) q[0];\nu3(0,0,pi/4) q[2];\nu2(0,pi) q[2];\nu2(0,pi) q[5];\ncx q[5],q[3];\ncx q[5],q[4];\nu2(0,pi) q[6];\nu3(pi,0,pi) q[6];\nu2(0,pi) q[6];\nu2(0,pi) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[5];\ncx q[4],q[5];\nu3(0,0,pi/8) q[5];\ncx q[4],q[5];\nu3(pi,0,pi) q[4];\nu2(0,pi) q[4];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/16) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/16) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/16) q[3];\nu3(0,0,pi/16) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/16) q[5];\ncx q[3],q[5];\nu3(0,0,pi/16) q[5];\ncx q[3],q[5];\nu3(pi,0,pi) q[3];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\nu3(0,0,-pi/16) q[6];\ncx q[2],q[6];\nu3(0,0,pi/32) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/32) q[6];\ncx q[2],q[6];\nu3(0,0,-pi/32) q[2];\nu3(0,0,pi/32) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/32) q[5];\ncx q[2],q[5];\nu3(0,0,pi/32) q[5];\ncx q[2],q[5];\nu3(pi,0,pi) q[2];\nu3(0,0,-pi/32) q[6];\ncx q[1],q[6];\nu3(0,0,pi/64) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/64) q[6];\ncx q[1],q[6];\nu3(0,0,-pi/64) q[1];\nu3(0,0,pi/64) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/64) q[5];\ncx q[1],q[5];\nu3(0,0,pi/64) q[5];\ncx q[1],q[5];\nu3(pi,0,pi) q[1];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\ncx q[5],q[3];\nu3(0,0,-pi/4) q[3];\nu3(0,0,pi/4) q[5];\ncx q[5],q[3];\ncx q[5],q[3];\nu3(pi,0,pi) q[5];\nu3(pi,0,pi) q[5];\ncx q[5],q[3];\ncx q[5],q[4];\nu2(0,pi) q[4];\ncx q[3],q[4];\nu3(0,0,-pi/4) q[4];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu2(0,pi) q[5];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\ncx q[3],q[4];\nu3(0,0,pi/4) q[3];\nu3(0,0,-pi/4) q[4];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\nu2(0,pi) q[4];\ncx q[5],q[3];\nu3(0,0,-pi/4) q[3];\nu3(0,0,pi/4) q[5];\ncx q[5],q[3];\ncx q[5],q[3];\nu3(pi,0,pi) q[5];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[1],q[5];\nu3(0,0,pi/8) q[5];\ncx q[2],q[5];\nu2(0,pi) q[2];\ncx q[1],q[2];\nu3(0,0,-pi/4) q[2];\nu3(0,0,-pi/8) q[5];\ncx q[0],q[5];\ncx q[0],q[2];\nu3(0,0,pi/4) q[2];\ncx q[1],q[2];\nu3(0,0,pi/4) q[1];\nu3(0,0,-pi/4) q[2];\ncx q[0],q[2];\ncx q[0],q[1];\nu3(0,0,pi/4) q[0];\nu3(0,0,-pi/4) q[1];\ncx q[0],q[1];\ncx q[0],q[1];\nu3(pi,0,pi) q[0];\nu3(pi,0,pi) q[0];\nu3(pi,0,pi) q[1];\nu3(0,0,pi/4) q[2];\nu2(0,pi) q[2];\nu3(pi,0,pi) q[2];\nu2(0,pi) q[5];\ncx q[5],q[3];\nu3(pi,0,pi) q[3];\ncx q[5],q[4];\nu3(pi,0,pi) q[4];\nu3(0,0,-pi/64) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\ncx q[4],q[5];\nu3(0,0,-pi/8) q[5];\ncx q[4],q[5];\nu3(pi,0,pi) q[4];\nu2(0,pi) q[4];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/16) q[6];\ncx q[5],q[6];\nu3(0,0,pi/16) q[6];\ncx q[3],q[6];\nu3(0,0,pi/16) q[3];\nu3(0,0,-pi/16) q[6];\ncx q[5],q[6];\nu3(0,0,pi/16) q[5];\ncx q[3],q[5];\nu3(0,0,-pi/16) q[5];\ncx q[3],q[5];\nu3(pi,0,pi) q[3];\nu2(0,pi) q[3];\nu3(0,0,pi/16) q[6];\ncx q[2],q[6];\nu3(0,0,-pi/32) q[6];\ncx q[5],q[6];\nu3(0,0,pi/32) q[6];\ncx q[2],q[6];\nu3(0,0,pi/32) q[2];\nu3(0,0,-pi/32) q[6];\ncx q[5],q[6];\nu3(0,0,pi/32) q[5];\ncx q[2],q[5];\nu3(0,0,-pi/32) q[5];\ncx q[2],q[5];\nu3(pi,0,pi) q[2];\nu2(0,pi) q[2];\nu3(0,0,pi/32) q[6];\ncx q[1],q[6];\nu3(0,0,-pi/64) q[6];\ncx q[5],q[6];\nu3(0,0,pi/64) q[6];\ncx q[1],q[6];\nu3(0,0,pi/64) q[1];\nu3(0,0,-pi/64) q[6];\ncx q[5],q[6];\nu3(0,0,pi/64) q[5];\ncx q[1],q[5];\nu3(0,0,-pi/64) q[5];\ncx q[1],q[5];\nu3(pi,0,pi) q[1];\nu2(0,pi) q[1];\nu3(0,0,pi/64) q[6];\ncx q[0],q[6];\nu3(0,0,-pi/64) q[6];\ncx q[5],q[6];\nu3(0,0,pi/64) q[6];\ncx q[0],q[6];\nu3(0,0,pi/64) q[0];\nu3(0,0,-pi/64) q[6];\ncx q[5],q[6];\nu3(0,0,pi/64) q[5];\ncx q[0],q[5];\nu3(0,0,-pi/64) q[5];\ncx q[0],q[5];\nu3(pi,0,pi) q[0];\nu2(0,pi) q[0];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\nu3(0,0,pi/64) q[6];\nu2(0,pi) q[6];\nu2(0,pi) q[6];\nu3(pi,0,pi) q[6];\nu2(0,pi) q[6];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "Analyze the following 7-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\nu2(0,pi) q[0];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu2(0,pi) q[3];\nu2(0,pi) q[3];\nu2(0,pi) q[4];\nu2(0,pi) q[4];\nu2(0,pi) q[5];\nu3(pi,0,pi) q[6];\nu2(0,pi) q[6];\ncx q[2],q[6];\nu2(0,pi) q[2];\ncx q[5],q[6];\nu2(0,pi) q[5];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "Analyze the following 6-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu2(0,pi) q[3];\nu2(0,pi) q[3];\nu2(0,pi) q[4];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\ncx q[0],q[5];\nu2(0,pi) q[0];\ncx q[2],q[5];\nu2(0,pi) q[2];\ncx q[4],q[5];\nu2(0,pi) q[4];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "Analyze the following 7-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\nu2(0,pi) q[0];\nu3(0,0,pi/8) q[0];\nu2(0,pi) q[1];\nu3(0,0,pi/8) q[1];\nu2(0,pi) q[2];\nu3(0,0,pi/8) q[2];\nu2(0,pi) q[3];\nu3(0,0,pi/8) q[3];\nu2(0,pi) q[4];\nu3(0,0,pi/8) q[4];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[5];\nu3(pi,0,pi) q[6];\ncx q[0],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[0],q[6];\nu3(0,0,pi/8) q[6];\ncx q[1],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[1],q[6];\nu3(0,0,pi/8) q[1];\nu3(0,0,pi/8) q[6];\ncx q[1],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[1],q[6];\nu3(0,0,pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,pi/8) q[2];\nu3(0,0,pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,pi/8) q[2];\nu3(0,0,pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,pi/8) q[2];\nu3(0,0,pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[2],q[6];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/8) q[3];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/8) q[3];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/8) q[3];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/8) q[3];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/8) q[3];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/8) q[3];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,pi/8) q[3];\nu3(0,0,pi/8) q[6];\ncx q[3],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[3],q[6];\ncx q[2],q[3];\ncx q[3],q[2];\ncx q[2],q[3];\nu3(0,0,-pi/8) q[2];\nu3(0,0,-pi/16) q[3];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,pi/8) q[4];\nu3(0,0,pi/8) q[6];\ncx q[4],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[4],q[6];\ncx q[1],q[4];\ncx q[4],q[1];\ncx q[1],q[4];\nu3(0,0,-pi/4) q[1];\nu3(0,0,-pi/32) q[4];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,pi/8) q[5];\nu3(0,0,pi/8) q[6];\ncx q[5],q[6];\nu3(0,0,-pi/8) q[6];\ncx q[5],q[6];\ncx q[0],q[5];\ncx q[5],q[0];\ncx q[0],q[5];\nu2(0,pi) q[0];\ncx q[1],q[0];\nu3(0,0,pi/4) q[0];\ncx q[1],q[0];\nu3(0,0,-pi/4) q[0];\nu2(0,pi) q[1];\ncx q[2],q[0];\nu3(0,0,pi/8) q[0];\ncx q[2],q[0];\nu3(0,0,-pi/8) q[0];\nu3(0,0,-pi/4) q[2];\ncx q[2],q[1];\nu3(0,0,pi/4) q[1];\ncx q[2],q[1];\nu3(0,0,-pi/4) q[1];\nu2(0,pi) q[2];\ncx q[3],q[0];\nu3(0,0,pi/16) q[0];\ncx q[3],q[0];\nu3(0,0,-pi/16) q[0];\nu3(0,0,-pi/8) q[3];\ncx q[3],q[1];\nu3(0,0,pi/8) q[1];\ncx q[3],q[1];\nu3(0,0,-pi/8) q[1];\nu3(0,0,-pi/4) q[3];\ncx q[3],q[2];\nu3(0,0,pi/4) q[2];\ncx q[3],q[2];\nu3(0,0,-pi/4) q[2];\nu2(0,pi) q[3];\ncx q[4],q[0];\nu3(0,0,pi/32) q[0];\ncx q[4],q[0];\nu3(0,0,-pi/32) q[0];\nu3(0,0,-pi/16) q[4];\ncx q[4],q[1];\nu3(0,0,pi/16) q[1];\ncx q[4],q[1];\nu3(0,0,-pi/16) q[1];\nu3(0,0,-pi/8) q[4];\ncx q[4],q[2];\nu3(0,0,pi/8) q[2];\ncx q[4],q[2];\nu3(0,0,-pi/8) q[2];\nu3(0,0,-pi/4) q[4];\ncx q[4],q[3];\nu3(0,0,pi/4) q[3];\ncx q[4],q[3];\nu3(0,0,-pi/4) q[3];\nu2(0,pi) q[4];\nu3(0,0,-pi/64) q[5];\ncx q[5],q[0];\nu3(0,0,pi/64) q[0];\ncx q[5],q[0];\nu3(0,0,-pi/64) q[0];\nu3(0,0,-pi/32) q[5];\ncx q[5],q[1];\nu3(0,0,pi/32) q[1];\ncx q[5],q[1];\nu3(0,0,-pi/32) q[1];\nu3(0,0,-pi/16) q[5];\ncx q[5],q[2];\nu3(0,0,pi/16) q[2];\ncx q[5],q[2];\nu3(0,0,-pi/16) q[2];\nu3(0,0,-pi/8) q[5];\ncx q[5],q[3];\nu3(0,0,pi/8) q[3];\ncx q[5],q[3];\nu3(0,0,-pi/8) q[3];\nu3(0,0,-pi/4) q[5];\ncx q[5],q[4];\nu3(0,0,pi/4) q[4];\ncx q[5],q[4];\nu3(0,0,-pi/4) q[4];\nu2(0,pi) q[5];\nu3(0,0,pi/8) q[6];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T6", "task_code": "J1_reverse", "task_name": "Reverse Engineering", "workflow_stage": "Understand", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "Analyze the following 6-qubit quantum circuit and identify what algorithm or subroutine it implements.\n\nCircuit (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nu2(0,pi) q[0];\nu2(0,pi) q[0];\nu2(0,pi) q[1];\nu2(0,pi) q[1];\nu2(0,pi) q[2];\nu2(0,pi) q[2];\nu2(0,pi) q[3];\nu2(0,pi) q[3];\nu2(0,pi) q[4];\nu2(0,pi) q[4];\nu3(pi,0,pi) q[5];\nu2(0,pi) q[5];\nu3(pi,0,pi) q[5];\n```\n\nWrite a function `solve()` that returns a dictionary with:\n  - 'algorithm': string name of the algorithm (e.g., 'qft', 'grover_diffusion', 'ghz', 'bell', 'teleportation', 'swap_test', 'bernstein_vazirani', 'deutsch_jozsa', 'phase_estimation_core', 'inverse_qft')\n  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)\n\nValid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nt q[1];\ns q[1];\ncz q[2],q[3];\ns q[1];\ns q[2];\ncz q[3],q[0];\nrz(4.124196450638081) q[3];\nrz(5.565039855165545) q[0];\ns q[0];\ncx q[0],q[1];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nt q[1];\ns q[1];\ncz q[2],q[3];\ns q[1];\ns q[2];\ncz q[3],q[0];\nrz(4.124196450638081) q[3];\nrz(6.15661964562299) q[0];\ns q[0];\ncx q[0],q[1];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nry(0.15020205251846416) q[2];\nx q[1];\ns q[2];\nt q[3];\nt q[1];\ncx q[0],q[1];\nx q[3];\ns q[1];\nz q[1];\ncx q[1],q[0];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nry(0.15020205251846416) q[2];\nx q[1];\ns q[2];\nt q[3];\nt q[1];\ncx q[0],q[1];\nx q[3];\ns q[1];\nz q[1];\ncx q[1],q[0];\ns q[3];\ns q[3];\nz q[3];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ny q[3];\ncx q[2],q[1];\nry(1.5391012516365692) q[1];\nry(1.8903295557165234) q[2];\ns q[0];\nh q[0];\ncz q[2],q[3];\nz q[2];\nx q[3];\nt q[1];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nt q[3];\ncx q[2],q[1];\nry(1.5391012516365692) q[1];\nry(1.8903295557165234) q[2];\ns q[0];\nh q[0];\ncz q[2],q[3];\nz q[2];\nx q[3];\nt q[1];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nh q[1];\ny q[0];\nx q[1];\nrz(4.223213152883283) q[2];\nrx(5.970381465087641) q[1];\nz q[0];\nz q[0];\ny q[1];\nry(4.464956090633724) q[1];\ncz q[0],q[1];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\nh q[1];\ny q[0];\nx q[1];\nrz(4.223213152883283) q[2];\nrx(5.970381465087641) q[1];\nz q[0];\nz q[0];\ny q[1];\nry(4.464956090633724) q[1];\ncz q[0],q[1];\nh q[3];\nh q[3];\nh q[2];\nh q[2];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[0],q[1];\nz q[1];\nx q[2];\ncz q[2],q[1];\nt q[1];\ncz q[1],q[0];\ncx q[0],q[3];\ny q[0];\nry(1.705047798632293) q[1];\ny q[2];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[0],q[1];\nz q[1];\nx q[2];\ncz q[2],q[1];\nt q[1];\ncz q[1],q[0];\ncx q[0],q[3];\ny q[0];\nry(2.0760527595901395) q[1];\ny q[2];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\ncx q[3],q[5];\nt q[2];\nh q[4];\nx q[0];\ncz q[3],q[2];\nt q[5];\ncz q[1],q[3];\nry(3.5929563116952115) q[0];\nrz(3.4324964786593237) q[0];\ns q[4];\ncx q[4],q[1];\nt q[2];\ncx q[0],q[4];\nrz(5.687740598132069) q[5];\ny q[0];\nrz(4.962966954193391) q[1];\ncz q[1],q[3];\nt q[3];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\ncx q[3],q[5];\nt q[2];\nh q[4];\nx q[0];\ncz q[3],q[2];\nt q[5];\ncz q[1],q[3];\nry(3.5929563116952115) q[0];\nrz(3.4324964786593237) q[0];\ns q[4];\ncx q[4],q[1];\nt q[2];\ncx q[0],q[4];\nrz(5.687740598132069) q[5];\ny q[0];\nrz(5.3488148949898795) q[1];\ncz q[1],q[3];\nt q[3];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nrx(0.6428373601854076) q[4];\ncx q[2],q[0];\nh q[5];\ncz q[0],q[3];\ns q[0];\ny q[4];\ny q[5];\nt q[1];\ncz q[0],q[1];\ncx q[1],q[2];\ncx q[4],q[3];\nt q[4];\ncz q[2],q[0];\nx q[3];\ncz q[2],q[0];\ncz q[3],q[0];\nh q[0];\ncx q[0],q[1];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nrx(0.6428373601854076) q[4];\ncx q[2],q[0];\nh q[5];\ncz q[0],q[3];\ns q[0];\ny q[4];\ny q[5];\nt q[1];\ncz q[0],q[1];\ncx q[1],q[2];\ncx q[4],q[3];\nt q[4];\ncz q[2],q[0];\nx q[3];\ncz q[2],q[0];\ncz q[3],q[0];\nh q[0];\ncx q[0],q[1];\nh q[2];\nh q[2];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\ny q[5];\nry(3.834887656844354) q[2];\nx q[0];\ny q[5];\ncx q[4],q[2];\nh q[0];\ns q[0];\nz q[0];\ncz q[0],q[2];\nx q[5];\ncz q[1],q[2];\nh q[2];\ncz q[3],q[4];\nh q[4];\nt q[3];\nx q[0];\nrx(3.0398623580969213) q[1];\nrx(5.597481013744184) q[1];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\ny q[5];\nry(3.834887656844354) q[2];\nx q[0];\ny q[5];\ncx q[4],q[2];\nh q[0];\ns q[0];\nz q[0];\ncz q[0],q[2];\nx q[5];\ncz q[1],q[2];\nh q[2];\ncz q[3],q[4];\nh q[4];\nh q[3];\nx q[0];\nrx(3.0398623580969213) q[1];\nrx(5.597481013744184) q[1];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nx q[0];\ns q[4];\ncz q[3],q[1];\nz q[2];\ncx q[0],q[4];\nry(5.198606068864962) q[2];\nrx(0.7036137925742918) q[3];\nh q[0];\nrz(0.12030840945657001) q[5];\nx q[1];\ns q[1];\ny q[5];\ny q[0];\ny q[0];\nrz(2.382861097058146) q[1];\ncx q[0],q[5];\nt q[4];\ncx q[2],q[1];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nx q[0];\ns q[4];\ncz q[3],q[1];\nz q[2];\ncx q[0],q[4];\nry(5.198606068864962) q[2];\nrx(0.7036137925742918) q[3];\nh q[0];\nrz(0.12030840945657001) q[5];\nx q[1];\ns q[1];\ny q[5];\ny q[0];\ny q[0];\nrz(2.382861097058146) q[1];\ncx q[0],q[5];\nt q[4];\ncx q[2],q[1];\nh q[2];\nh q[2];\nh q[0];\nh q[0];\nh q[3];\nh q[3];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nry(4.374501019211292) q[5];\ns q[0];\ny q[5];\nry(3.504125488335103) q[3];\ns q[3];\nt q[0];\nx q[3];\ny q[2];\ncz q[4],q[0];\nrz(0.28223736532698923) q[0];\ncx q[2],q[4];\ns q[4];\ns q[3];\nry(0.590853250194255) q[5];\nt q[1];\ns q[4];\ncz q[3],q[0];\nt q[5];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[6];\nry(4.374501019211292) q[5];\ns q[0];\ny q[5];\nry(3.504125488335103) q[3];\ns q[3];\nt q[0];\nx q[3];\ny q[2];\ncz q[4],q[0];\nrz(0.28223736532698923) q[0];\ncx q[2],q[4];\ns q[4];\ns q[3];\nry(0.590853250194255) q[5];\nt q[1];\ns q[4];\ncz q[3],q[0];\nrz(0.9534354917268888) q[3];\nt q[5];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ns q[5];\nx q[2];\ncz q[3],q[0];\ncz q[1],q[3];\ncz q[4],q[9];\nz q[0];\nt q[0];\nry(1.381243078207626) q[2];\nh q[7];\nx q[2];\ns q[2];\ny q[4];\nh q[2];\nx q[4];\ny q[0];\nz q[6];\ncz q[8],q[9];\nrx(3.089994700024885) q[8];\ncz q[9],q[0];\nh q[3];\nz q[6];\nry(1.1479538098857254) q[5];\ny q[5];\nz q[3];\ny q[4];\nrx(0.2307321825133641) q[6];\nrz(0.47122629548655287) q[4];\ncz q[8],q[6];\ncx q[5],q[6];\nh q[6];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ns q[5];\nx q[2];\ncz q[3],q[0];\ncz q[1],q[3];\ncz q[4],q[9];\nz q[0];\nt q[0];\nry(1.381243078207626) q[2];\nh q[7];\nx q[2];\ns q[2];\ny q[4];\nh q[2];\nx q[4];\ny q[0];\nz q[6];\ncz q[8],q[9];\nrx(3.089994700024885) q[8];\ncz q[9],q[0];\nh q[3];\ns q[6];\nry(1.1479538098857254) q[5];\ny q[5];\nz q[3];\ny q[4];\nrx(0.2307321825133641) q[6];\nrz(0.47122629548655287) q[4];\ncz q[8],q[6];\ncx q[5],q[6];\nh q[6];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\nz q[4];\ns q[9];\ncx q[1],q[3];\nx q[9];\ncz q[7],q[4];\ncx q[7],q[5];\ncx q[2],q[6];\nt q[1];\ncx q[2],q[3];\ny q[1];\nh q[9];\nx q[7];\nx q[6];\ncz q[4],q[7];\ncz q[5],q[1];\ncx q[3],q[1];\nrx(1.366671214571527) q[1];\nz q[4];\ncx q[6],q[7];\nh q[8];\nz q[1];\nz q[0];\ny q[5];\nz q[0];\nh q[2];\ncz q[2],q[3];\ny q[5];\nx q[6];\nz q[8];\ncz q[6],q[0];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\nz q[4];\ns q[9];\ncx q[1],q[3];\nx q[9];\ncz q[7],q[4];\ncx q[7],q[5];\ncx q[2],q[6];\nt q[1];\ncx q[2],q[3];\ny q[1];\nh q[9];\nx q[7];\nx q[6];\ncz q[4],q[7];\ncz q[5],q[1];\ncx q[3],q[1];\nrx(1.366671214571527) q[1];\nz q[4];\ncx q[6],q[7];\nh q[8];\nz q[1];\nz q[0];\ny q[5];\nz q[0];\nh q[2];\ncz q[2],q[3];\ny q[5];\nx q[6];\nz q[8];\ncz q[6],q[0];\nh q[0];\nh q[0];\nx q[9];\nx q[9];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ns q[0];\ncz q[7],q[5];\nh q[7];\ncx q[3],q[4];\nrz(5.736650091825691) q[6];\nx q[0];\ns q[4];\ns q[0];\ncx q[2],q[4];\nry(1.0463845822067088) q[8];\ncx q[5],q[2];\nz q[9];\nz q[4];\ny q[7];\nh q[9];\ny q[5];\ny q[5];\nt q[3];\ncx q[1],q[4];\nz q[9];\nz q[3];\nrz(5.56552043588244) q[6];\nrx(0.17981425537182835) q[9];\nt q[6];\nz q[2];\ncz q[3],q[2];\nry(1.2165291867695998) q[9];\ncz q[8],q[3];\ncx q[6],q[7];\ncx q[4],q[8];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ns q[0];\ncz q[7],q[5];\nh q[7];\ncx q[3],q[4];\nrz(5.736650091825691) q[6];\nx q[0];\ns q[4];\ns q[0];\ncx q[2],q[4];\nry(1.0463845822067088) q[8];\ncx q[5],q[2];\nz q[9];\nz q[4];\ny q[7];\nh q[9];\nz q[5];\ny q[5];\nt q[3];\ncx q[1],q[4];\nz q[9];\nz q[3];\nrz(5.56552043588244) q[6];\nrx(0.17981425537182835) q[9];\nt q[6];\nz q[2];\ncz q[3],q[2];\nry(1.2165291867695998) q[9];\ncz q[8],q[3];\ncx q[6],q[7];\ncx q[4],q[8];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ncz q[5],q[7];\nz q[8];\nrx(5.119827056542912) q[7];\nz q[9];\nt q[4];\ncx q[1],q[4];\ncz q[0],q[5];\nrx(5.9260388984972) q[6];\nh q[6];\ncz q[7],q[6];\nrz(0.14113982523033736) q[6];\ncx q[1],q[2];\ncx q[4],q[9];\nrz(3.196168710917012) q[9];\ns q[4];\ny q[4];\nry(5.274683918594714) q[1];\ncx q[4],q[6];\nh q[7];\ncx q[3],q[9];\nt q[3];\nt q[8];\ny q[1];\nrx(2.902055727548061) q[2];\nz q[4];\nrz(3.920918573880772) q[7];\nt q[2];\nry(0.3958564474050542) q[8];\nry(4.876942177709919) q[0];\ncx q[8],q[4];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ncz q[5],q[7];\nz q[8];\nrx(5.119827056542912) q[7];\nz q[9];\nt q[4];\ncx q[1],q[4];\ncz q[0],q[5];\nrx(5.9260388984972) q[6];\nh q[6];\ncz q[7],q[6];\nrz(0.14113982523033736) q[6];\ncx q[1],q[2];\ncx q[4],q[9];\nrz(3.196168710917012) q[9];\ns q[4];\ny q[4];\nry(5.274683918594714) q[1];\ncx q[4],q[6];\nh q[7];\ncx q[3],q[9];\nt q[3];\nt q[8];\ny q[1];\nrx(2.902055727548061) q[2];\nz q[4];\nrz(3.920918573880772) q[7];\nt q[2];\nry(0.3958564474050542) q[8];\nry(4.876942177709919) q[0];\ncx q[8],q[4];\nh q[0];\nh q[0];\ns q[4];\ns q[4];\nz q[4];\nh q[5];\nh q[5];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ns q[4];\ny q[6];\nh q[3];\nrx(0.13900911153489012) q[1];\nt q[4];\nh q[8];\nrx(4.835408776863877) q[7];\nz q[7];\ncz q[8],q[2];\ncx q[7],q[4];\ncz q[7],q[1];\nrz(0.24307604970574218) q[8];\ns q[6];\nz q[7];\nx q[6];\nrx(4.394326520326433) q[9];\nx q[4];\nrx(2.9117432417950204) q[9];\nx q[5];\nrx(2.142969749756436) q[5];\ncz q[6],q[8];\ncx q[4],q[5];\nt q[9];\nrx(4.653306259731393) q[1];\nh q[6];\ny q[4];\nx q[4];\ncx q[3],q[2];\ncx q[8],q[0];\ns q[2];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ns q[4];\ny q[6];\nh q[3];\nrx(0.13900911153489012) q[1];\nt q[4];\nh q[8];\nrx(4.835408776863877) q[7];\nz q[7];\ncz q[8],q[2];\ncx q[7],q[4];\ncz q[7],q[1];\nrz(0.24307604970574218) q[8];\ns q[6];\nz q[7];\nx q[6];\nrx(4.394326520326433) q[9];\nx q[4];\nrx(2.9117432417950204) q[9];\nx q[5];\nrx(2.142969749756436) q[5];\ncz q[6],q[8];\ncx q[4],q[5];\nt q[9];\nrx(4.653306259731393) q[1];\nh q[6];\ny q[4];\nx q[4];\ncx q[2],q[3];\ncx q[8],q[0];\ns q[2];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\ncx q[0],q[10];\ncz q[5],q[2];\ncz q[10],q[4];\ncx q[1],q[0];\ny q[0];\ncz q[6],q[4];\nry(3.1849367347398965) q[4];\ncx q[1],q[6];\ns q[10];\ny q[6];\ny q[2];\ncz q[8],q[4];\ny q[8];\nx q[8];\nrx(0.35962690705794126) q[6];\ns q[5];\nt q[0];\nx q[6];\nx q[1];\nh q[5];\ncz q[8],q[11];\nx q[11];\nz q[3];\nrx(4.070412921493407) q[2];\nt q[11];\ncx q[0],q[6];\ny q[0];\nry(2.5699231395662565) q[8];\nz q[6];\nt q[2];\nh q[10];\ncz q[1],q[7];\nrz(5.6508062204013285) q[1];\ncx q[6],q[1];\nrx(0.4850419713763551) q[7];\ncz q[4],q[2];\nt q[1];\ns q[8];\nz q[5];\nt q[6];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nh q[2];\nrz(3.9856967221918107) q[3];\nh q[4];\ncx q[5],q[2];\nrz(-0.9288202679036139) q[2];\nrx(-3*pi/4) q[2];\nrz(pi/2) q[5];\nry(-pi/2) q[5];\nh q[7];\ncx q[0],q[10];\ncx q[1],q[0];\nry(pi) q[0];\nrz(pi/4) q[0];\ncx q[10],q[4];\ncx q[6],q[4];\ncx q[1],q[6];\nx q[1];\ncx q[1],q[7];\nrz(5.6508062204013285) q[1];\nry(3.4311082471990075) q[4];\nry(pi) q[6];\nrx(3.5012195606477343) q[6];\ncx q[0],q[6];\nry(pi) q[0];\nrz(5*pi/4) q[6];\ncx q[6],q[1];\nrz(pi/4) q[1];\nh q[7];\nrx(0.4850419713763551) q[7];\ncx q[8],q[4];\nh q[4];\ncx q[4],q[2];\nh q[2];\nrz(-pi) q[8];\nrz(pi/2) q[10];\nh q[10];\nh q[11];\ncx q[8],q[11];\nry(2.5699231395662565) q[8];\nrz(pi/2) q[8];\nry(2.3079151298403477) q[11];\nrz(pi/4) q[11];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nrx(5.92550020688181) q[1];\nz q[2];\ns q[3];\nx q[3];\ncx q[9],q[10];\nx q[10];\nry(6.208256068892496) q[4];\nx q[3];\ncx q[1],q[6];\ncz q[6],q[3];\nz q[8];\nry(0.19199770660329826) q[9];\nrz(4.713532602908841) q[9];\nz q[3];\ncz q[3],q[10];\nx q[3];\ns q[1];\nh q[8];\ncx q[4],q[2];\nrx(5.301326267231974) q[9];\nh q[7];\ns q[6];\ny q[4];\nry(1.9115838441514372) q[2];\ncx q[0],q[4];\nh q[0];\nrx(3.057876950368099) q[5];\nry(5.859570670216837) q[3];\ncx q[2],q[3];\ncz q[4],q[3];\nrz(2.2917904672326466) q[9];\ncx q[8],q[9];\ns q[2];\ny q[6];\nry(3.7277276145540488) q[1];\ncz q[5],q[8];\ncx q[9],q[8];\ny q[10];\nx q[8];\ns q[7];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nrx(5.92550020688181) q[1];\nrz(pi) q[2];\nrz(3*pi/2) q[3];\nh q[3];\nry(6.208256068892496) q[4];\ncx q[4],q[2];\nry(1.9115838441514372) q[2];\nry(pi) q[4];\ncx q[0],q[4];\nh q[0];\nrx(3.057876950368099) q[5];\ncx q[1],q[6];\nrz(pi/2) q[1];\nry(3.7277276145540488) q[1];\ncx q[6],q[3];\nh q[3];\nrz(pi/2) q[6];\nry(pi) q[6];\nx q[0];\nx q[0];\nh q[7];\nrz(pi/2) q[7];\nry(pi/2) q[8];\ncx q[9],q[10];\nrz(-3.1402537581828645) q[9];\nry(0.7898614794354343) q[9];\nrz(-2.420905763480704) q[9];\nx q[11];\nx q[11];\ncx q[8],q[9];\nh q[8];\ncx q[5],q[8];\nh q[8];\ncx q[9],q[8];\nx q[8];\nry(-pi/2) q[10];\ncx q[3],q[10];\nx q[3];\nry(5.859570670216837) q[3];\ncx q[2],q[3];\nrz(pi/2) q[2];\nh q[3];\ncx q[4],q[3];\nh q[3];\nh q[10];\nry(pi) q[10];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nh q[3];\nz q[1];\ns q[3];\nz q[11];\ncz q[4],q[2];\nx q[9];\ny q[11];\nx q[11];\ny q[8];\ncz q[8],q[5];\ncz q[5],q[2];\ns q[5];\nt q[8];\ncx q[5],q[3];\ncx q[9],q[0];\ncx q[7],q[1];\nry(4.69553845940479) q[9];\ncz q[4],q[2];\ny q[4];\ncx q[10],q[6];\nx q[0];\ny q[0];\nx q[5];\ns q[0];\nrz(4.7996101619797065) q[4];\nrx(2.8433055314440168) q[4];\nz q[0];\nry(2.9601008427458995) q[7];\ncx q[0],q[2];\nx q[2];\ns q[9];\ny q[6];\ncx q[4],q[1];\nz q[10];\nt q[7];\ns q[4];\nrz(0.48415689123877803) q[5];\ny q[9];\nry(1.089133865252038) q[0];\ncx q[6],q[8];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nrz(pi) q[1];\nh q[2];\nh q[3];\nrz(2.3347574695349964) q[3];\nrz(-1.6580175083899134) q[4];\nrx(-0.2982871221457766) q[4];\nh q[5];\ncx q[7],q[1];\ncx q[4],q[1];\nrz(pi/2) q[4];\nry(2.9601008427458995) q[7];\nrz(pi/4) q[7];\nry(4.0781534851299766) q[8];\ncx q[8],q[5];\nh q[5];\ncx q[5],q[2];\nh q[2];\nrz(pi/2) q[5];\ncx q[5],q[3];\nx q[5];\nrz(0.48415689123877803) q[5];\nrz(pi/4) q[8];\nx q[9];\ncx q[9],q[0];\nrz(pi/2) q[0];\ncx q[0],q[2];\nry(1.089133865252038) q[0];\nx q[2];\nry(1.5539458058149966) q[9];\nrz(-pi/2) q[9];\ncx q[10],q[6];\nry(pi) q[6];\ncx q[6],q[8];\nrz(4.04943093227983) q[10];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\ncz q[10],q[3];\nrx(3.565912955911002) q[2];\nrz(2.4258308371489203) q[6];\ncz q[6],q[7];\nx q[1];\nh q[0];\ny q[8];\nz q[4];\nx q[11];\nt q[4];\ns q[8];\nrz(4.97320825750158) q[3];\ncx q[10],q[4];\nt q[6];\nry(3.5048648242575777) q[10];\ncx q[6],q[4];\nz q[1];\nrz(1.9322388056630297) q[7];\ncz q[3],q[6];\ncx q[7],q[2];\ncx q[7],q[5];\nrx(2.8673857507137934) q[5];\nx q[10];\ncx q[10],q[4];\ncx q[7],q[5];\nz q[5];\nt q[1];\ncz q[6],q[4];\ncz q[1],q[6];\nh q[6];\nh q[8];\ncz q[7],q[11];\nrx(3.6803672216376744) q[10];\nh q[0];\nh q[1];\ncx q[2],q[1];\nz q[3];\ny q[10];\ncx q[11],q[3];\ncx q[10],q[11];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nx q[1];\nrz(5*pi/4) q[1];\nrx(3.565912955911002) q[2];\nh q[3];\nrz(5*pi/4) q[4];\nrx(2.8673857507137934) q[5];\nh q[8];\nh q[8];\nrz(pi) q[5];\nrz(3.2112290005463686) q[6];\nh q[7];\ncx q[6],q[7];\nh q[7];\nrz(1.9322388056630297) q[7];\ncx q[7],q[2];\nrz(pi/2) q[8];\nry(-pi/2) q[8];\ncx q[10],q[3];\nh q[3];\nrz(8.114800911091372) q[3];\ncx q[10],q[4];\ncx q[6],q[4];\nh q[6];\ncx q[3],q[6];\nh q[6];\nry(3.5048648242575777) q[10];\nx q[10];\ncx q[10],q[4];\nh q[4];\ncx q[6],q[4];\nh q[4];\nh q[6];\ncx q[1],q[6];\nh q[1];\ncx q[2],q[1];\nrx(3.6803672216376744) q[10];\nry(pi) q[10];\nry(-pi/2) q[11];\ncx q[7],q[11];\nh q[11];\ns q[1];\ns q[1];\nz q[1];\ncx q[11],q[3];\ncx q[10],q[11];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nx q[2];\nt q[8];\ny q[4];\nrx(0.8212239749437135) q[6];\nh q[2];\nh q[3];\nz q[3];\nx q[6];\nx q[9];\ncx q[6],q[0];\nh q[2];\nt q[3];\ncx q[9],q[4];\ns q[7];\ny q[3];\ncz q[0],q[3];\nry(1.586927554328436) q[8];\ny q[7];\ny q[1];\ns q[7];\nry(1.234869319072365) q[3];\ncz q[6],q[2];\ny q[4];\nh q[6];\nt q[2];\ns q[1];\ny q[9];\ncx q[6],q[9];\nz q[11];\nh q[10];\nh q[7];\ncx q[10],q[7];\nz q[6];\nry(5.520680537892614) q[6];\nt q[1];\ns q[6];\ncz q[10],q[4];\ns q[3];\ncx q[10],q[6];\nrx(3.6820866227845843) q[10];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[12];\nrz(-3*pi/4) q[1];\nry(pi) q[1];\nry(-0.5868898936005222) q[2];\nrz(-pi) q[3];\nrx(-pi/4) q[3];\nry(pi) q[4];\nrx(3.9628166285335067) q[6];\ncx q[6],q[0];\ncx q[0],q[3];\nry(-2.194550350678991) q[3];\nrz(-pi/2) q[3];\ncx q[6],q[2];\nh q[2];\nrz(pi/4) q[2];\nh q[6];\nrz(-pi) q[7];\nry(-0.574707481610585) q[7];\nrz(pi/4) q[8];\nry(1.586927554328436) q[8];\nx q[9];\ncx q[9],q[4];\nry(pi) q[4];\nh q[4];\nry(pi) q[9];\ncx q[6],q[9];\nry(0.7625047692869729) q[6];\nrz(-pi/2) q[6];\nh q[10];\ncx q[10],q[7];\ncx q[10],q[4];\nh q[4];\ncx q[10],q[6];\nrx(3.6820866227845843) q[10];\nrz(pi) q[11];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nh q[0];\nz q[2];\nt q[13];\nt q[0];\nrz(5.024267334635643) q[12];\nry(1.798535968996919) q[11];\ncx q[5],q[1];\nh q[5];\ncx q[11],q[6];\nx q[1];\ncz q[7],q[8];\ny q[13];\ncx q[9],q[12];\ncz q[4],q[1];\ny q[0];\ncx q[0],q[6];\ncz q[8],q[3];\ncx q[13],q[7];\ny q[9];\ncz q[12],q[9];\ncz q[11],q[8];\nx q[5];\ncx q[5],q[3];\ny q[0];\nrx(2.3620671057185727) q[8];\ncz q[9],q[6];\nry(6.014813233512013) q[3];\nz q[6];\nry(1.251801085655153) q[1];\nrz(5.227142850173022) q[12];\nry(0.5892156730760137) q[7];\ncz q[4],q[11];\ncx q[3],q[4];\nz q[6];\ncz q[11],q[10];\nry(4.382101640568701) q[13];\ncz q[8],q[7];\ns q[12];\nh q[4];\ny q[8];\nx q[0];\nt q[5];\ncz q[0],q[11];\nt q[10];\nt q[5];\ncx q[6],q[11];\nry(3.128898118538559) q[5];\nt q[6];\nrz(5.904337709273202) q[12];\ncz q[4],q[11];\nx q[8];\ny q[10];\nrz(4.3730986066586315) q[3];\ncz q[2],q[13];\ny q[6];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nry(2.3571585650319706) q[0];\nrz(-pi/4) q[0];\nrz(pi) q[2];\nh q[3];\ncx q[5],q[1];\nry(-0.7053085425866642) q[1];\ncx q[4],q[1];\nh q[1];\nry(1.251801085655153) q[1];\nry(pi/2) q[5];\nh q[8];\ncx q[7],q[8];\nh q[8];\ncx q[8],q[3];\nh q[3];\ncx q[5],q[3];\nry(6.014813233512013) q[3];\nrz(pi/2) q[5];\nry(3.128898118538559) q[5];\nh q[8];\nrx(pi) q[9];\nh q[10];\nry(1.798535968996919) q[11];\ncx q[11],q[6];\ncx q[0],q[6];\nh q[6];\ncx q[11],q[8];\nh q[8];\nrx(2.3620671057185727) q[8];\nh q[11];\ncx q[4],q[11];\ncx q[3],q[4];\nrz(4.3730986066586315) q[3];\nh q[4];\nh q[11];\ncx q[11],q[10];\nry(2.0871287931858156) q[10];\nrz(3*pi/4) q[10];\nh q[11];\ncx q[0],q[11];\nh q[11];\nrz(-2.829714299338839) q[12];\nrx(-pi) q[12];\ncx q[9],q[12];\nrz(pi/2) q[9];\ncx q[9],q[6];\nh q[6];\ncx q[6],q[11];\nrz(pi/4) q[6];\nry(pi) q[6];\nh q[11];\ncx q[4],q[11];\nh q[11];\nrz(-1.4348900549129482) q[12];\nrz(pi/4) q[13];\nry(pi) q[13];\ncx q[13],q[7];\nry(0.5892156730760137) q[7];\nh q[7];\ncx q[8],q[7];\nh q[7];\nrz(-pi) q[8];\nry(4.382101640568701) q[13];\nh q[13];\ncx q[2],q[13];\nh q[13];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nh q[8];\ncx q[8],q[13];\nx q[11];\nz q[6];\ncx q[4],q[6];\ny q[7];\nrz(1.0333545112402156) q[7];\ns q[10];\nt q[2];\nt q[9];\nx q[5];\nz q[4];\ny q[4];\nx q[13];\ncz q[11],q[0];\ny q[3];\ncx q[5],q[9];\nt q[6];\nz q[13];\nz q[0];\nrz(3.683410660595319) q[6];\nh q[9];\nx q[9];\ncx q[9],q[2];\ncz q[1],q[13];\nz q[9];\ncz q[3],q[8];\nx q[9];\nz q[0];\nry(4.041467099982676) q[7];\ns q[0];\nt q[9];\ncx q[13],q[7];\ncx q[8],q[6];\nz q[0];\nrx(1.0261827657685991) q[4];\ncz q[2],q[13];\nz q[1];\ncx q[10],q[6];\ncz q[4],q[3];\ncz q[11],q[4];\nz q[4];\nx q[5];\ncx q[1],q[12];\ny q[4];\nx q[5];\nrx(2.3582214925279765) q[12];\ncx q[2],q[0];\nx q[2];\ny q[7];\nrz(1.3121359422204464) q[13];\ncz q[8],q[6];\nh q[11];\ncx q[5],q[11];\ncz q[3],q[10];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nh q[0];\nrz(pi/4) q[2];\nry(pi) q[3];\nx q[5];\nrz(pi) q[6];\ncx q[4],q[6];\ns q[13];\ns q[13];\nz q[13];\nrx(-2.115409887821194) q[4];\nrz(4.4688088239927675) q[6];\nrz(-1.0333545112402156) q[7];\nry(0.899874446392883) q[7];\nh q[8];\nrz(pi/4) q[9];\ncx q[5],q[9];\nry(pi/2) q[9];\ncx q[9],q[2];\nrz(-pi/4) q[9];\ns q[0];\ns q[0];\nz q[0];\nry(pi) q[9];\nrz(pi/2) q[10];\nx q[11];\ncx q[11],q[0];\nh q[8];\nh q[8];\nh q[0];\nrz(3*pi/2) q[0];\ncx q[8],q[13];\nh q[8];\ncx q[3],q[8];\nh q[3];\ncx q[4],q[3];\nh q[3];\nh q[4];\ns q[10];\ns q[10];\nz q[10];\nh q[8];\ncx q[8],q[6];\ncx q[10],q[6];\nh q[6];\ncx q[8],q[6];\nh q[6];\nh q[10];\ncx q[3],q[10];\nh q[10];\ncx q[11],q[4];\nry(pi/2) q[4];\nh q[11];\ncx q[5],q[11];\nrz(1.829456711369347) q[13];\nry(-pi/2) q[13];\ncx q[1],q[13];\nrz(pi) q[1];\ncx q[1],q[12];\nrx(2.3582214925279765) q[12];\nh q[13];\ncx q[13],q[7];\nry(pi) q[7];\nh q[13];\ncx q[2],q[13];\ncx q[2],q[0];\nx q[2];\nh q[13];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nrx(5.909672773479288) q[4];\nz q[12];\ny q[5];\ny q[12];\nrz(3.893759820960499) q[9];\nh q[1];\ns q[7];\nt q[9];\nrz(1.4826818544450509) q[0];\ncz q[1],q[8];\nh q[9];\nh q[10];\ns q[6];\ns q[8];\ncz q[9],q[4];\nry(5.19021539939376) q[9];\ns q[7];\ncx q[9],q[2];\nh q[12];\ncx q[9],q[6];\ny q[7];\nrz(0.6286555281683881) q[10];\ncx q[4],q[5];\ny q[5];\ny q[13];\nrz(1.2154038069920456) q[7];\nrx(2.284661366303957) q[8];\nrx(0.7273856311806477) q[2];\nrx(6.103324226420383) q[8];\nry(2.720578195198957) q[13];\ny q[11];\ns q[10];\nh q[7];\ns q[11];\nt q[11];\nry(4.766567335459742) q[9];\nrx(5.517622113126137) q[11];\ncz q[9],q[5];\nrz(2.738697716654763) q[4];\nz q[11];\nx q[7];\nry(0.9646067882777152) q[2];\ns q[9];\nh q[0];\nrz(2.793168155307437) q[3];\nrx(1.9924041166324504) q[8];\nx q[8];\ns q[5];\ncx q[5],q[4];\ny q[8];\nry(0.5910087089385755) q[11];\nz q[10];\ny q[11];\nt q[7];\ncz q[0],q[7];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nrz(1.4826818544450509) q[0];\nh q[0];\nh q[1];\nrz(2.793168155307437) q[3];\nrx(5.909672773479288) q[4];\nh q[4];\nry(pi) q[5];\nrz(pi/2) q[6];\nrz(1.9261888465977481) q[7];\nrx(-3*pi/4) q[7];\ncx q[0],q[7];\nh q[7];\nh q[8];\ncx q[1],q[8];\nry(2.526408075382306) q[8];\nrz(pi/2) q[8];\nrz(4.679157984357947) q[9];\nh q[9];\ncx q[9],q[4];\nh q[4];\ncx q[4],q[5];\nrz(2.738697716654763) q[4];\nry(pi) q[5];\nh q[5];\nry(5.19021539939376) q[9];\ncx q[9],q[2];\nrx(0.7273856311806477) q[2];\nry(0.9646067882777152) q[2];\ncx q[9],q[6];\nry(4.766567335459742) q[9];\ncx q[9],q[5];\nh q[5];\nrz(pi/2) q[5];\ncx q[5],q[4];\nrz(2.385235907207941) q[9];\nh q[10];\nrz(6.251973477053568) q[10];\nrz(-0.01607357669392062) q[11];\nry(0.9289231914110643) q[11];\nrz(1.045397163134572) q[11];\nry(-1.1667851935371683) q[12];\nry(-0.4210144583908362) q[13];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nx q[2];\ncx q[4],q[2];\ncz q[13],q[4];\nz q[11];\ny q[13];\nrz(4.302399126381679) q[10];\nrz(4.1424760047965155) q[13];\ny q[13];\nx q[6];\ncx q[12],q[5];\nh q[8];\ns q[3];\nh q[3];\nrx(3.608469115345701) q[4];\nrz(0.4706815419919275) q[5];\ncx q[2],q[9];\ncz q[6],q[11];\ncx q[0],q[2];\nz q[10];\ncz q[13],q[6];\nh q[1];\ny q[9];\ncz q[10],q[4];\ncz q[8],q[10];\ncz q[2],q[1];\nrz(0.3253659522240325) q[3];\nt q[7];\nrz(2.1448744966915387) q[2];\nrz(3.653797058759521) q[3];\nrx(4.5134000325238475) q[6];\ncx q[2],q[9];\nz q[8];\ncx q[10],q[1];\nz q[10];\nz q[4];\ncz q[5],q[13];\nrz(5.008883620445975) q[2];\ncz q[3],q[6];\nry(3.9148371446715857) q[0];\ncz q[4],q[5];\ncz q[5],q[12];\nt q[4];\ny q[8];\ncx q[0],q[13];\nt q[1];\ncz q[2],q[6];\nry(1.8554306488512342) q[6];\nx q[2];\ny q[10];\nt q[6];\ncz q[5],q[2];\nz q[3];\ncz q[8],q[5];\ncz q[4],q[2];\nz q[13];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nx q[2];\nrx(-pi/2) q[3];\nrz(-0.7332259694011363) q[3];\ncx q[4],q[2];\nh q[4];\nx q[6];\nrz(pi/4) q[7];\nh q[8];\ncx q[2],q[9];\ncx q[0],q[2];\nx q[5];\nx q[5];\nry(3.9148371446715857) q[0];\ncx q[2],q[1];\nh q[1];\nrz(7.153758117137514) q[2];\nry(pi) q[9];\ncx q[2],q[9];\nrz(10.585584433561266) q[10];\nx q[4];\nx q[4];\nry(pi/2) q[11];\ncx q[6],q[11];\nh q[6];\nh q[11];\ncx q[12],q[5];\nrz(0.4706815419919275) q[5];\nh q[12];\ncx q[13],q[4];\nrz(-2.6747161918338858) q[4];\ncx q[10],q[4];\nh q[4];\nrz(5*pi/4) q[4];\nh q[10];\ncx q[8],q[10];\nrx(pi) q[8];\nh q[10];\ncx q[10],q[1];\nrz(pi/4) q[1];\nry(pi) q[10];\nrz(2.1407093023830708) q[13];\ncx q[13],q[6];\nx q[8];\nx q[8];\nrz(-1.7697852746557388) q[6];\ncx q[3],q[6];\ncx q[2],q[6];\nry(-pi/2) q[2];\nry(2.856958331533456) q[6];\nrz(-3*pi/4) q[6];\nh q[13];\ncx q[5],q[13];\nh q[5];\ncx q[4],q[5];\nh q[5];\ncx q[5],q[12];\ncx q[5],q[2];\ncx q[4],q[2];\nh q[2];\nh q[5];\ncx q[8],q[5];\nh q[5];\nh q[12];\nh q[13];\ncx q[0],q[13];\nrz(pi) q[13];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T7", "task_code": "F1_equivalence", "task_name": "Equivalence Checking", "workflow_stage": "Verify", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?\n\nCircuit A (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nz q[1];\ncz q[2],q[1];\ny q[10];\nt q[7];\ncz q[2],q[1];\nrz(0.643490595348736) q[9];\nx q[13];\ncx q[13],q[2];\ns q[13];\nt q[10];\nx q[5];\ncz q[0],q[13];\ns q[10];\nry(4.13429172494234) q[7];\nry(4.808795900868258) q[8];\ncz q[4],q[11];\ncx q[8],q[4];\ncx q[0],q[11];\nrx(0.8874690506960367) q[13];\ny q[12];\ncx q[3],q[4];\nry(5.243404530617571) q[11];\nx q[5];\nh q[1];\nrx(4.1202803642574) q[3];\nrx(1.7512732600390188) q[5];\nx q[2];\nx q[12];\ncz q[1],q[5];\nx q[5];\nry(2.9805225904958217) q[5];\ny q[7];\ncx q[13],q[2];\ncx q[5],q[11];\nrx(4.157377053192782) q[3];\ny q[4];\ny q[11];\ncx q[12],q[0];\ncx q[8],q[3];\ns q[6];\nx q[2];\nry(4.637618986216838) q[5];\ns q[0];\nry(2.938812261503058) q[8];\ny q[5];\ncx q[6],q[11];\nrx(2.2883048916281914) q[13];\ns q[10];\nx q[8];\ncz q[0],q[6];\nrz(2.3464623514216814) q[12];\nz q[5];\ncz q[7],q[0];\ncx q[7],q[3];\ncz q[5],q[9];\n```\n\nCircuit B (OpenQASM 2.0):\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[14];\nry(pi/2) q[1];\nrx(2.3158776257216154) q[5];\nh q[5];\ncx q[1],q[5];\nry(-1.731866389888868) q[5];\nrz(pi/2) q[6];\nrz(pi/4) q[7];\nry(0.9926990713525468) q[7];\nry(5.555633855441001) q[8];\nrz(0.643490595348736) q[9];\nh q[9];\nry(3.913395927590104) q[10];\nrz(5*pi/4) q[10];\nh q[11];\ncx q[4],q[11];\ncx q[8],q[4];\ncx q[3],q[4];\nrx(8.277657417450182) q[3];\nry(pi) q[4];\ncx q[8],q[3];\nry(2.938812261503058) q[8];\nx q[8];\nh q[11];\nrz(-0.7951303021681118) q[12];\nx q[13];\ncx q[13],q[2];\nrz(pi/2) q[13];\nh q[13];\ncx q[0],q[13];\ncx q[0],q[11];\nry(5.243404530617571) q[11];\ncx q[5],q[11];\nrz(-pi) q[5];\nry(-1.4960263326270447) q[5];\ncx q[5],q[9];\nh q[9];\nry(pi) q[11];\ncx q[6],q[11];\nh q[6];\ncx q[12],q[0];\nrz(pi/2) q[0];\ncx q[0],q[6];\nh q[0];\nh q[6];\ncx q[7],q[0];\nh q[0];\ncx q[7],q[3];\nh q[13];\nrx(0.8874690506960367) q[13];\ncx q[13],q[2];\nrx(2.2883048916281914) q[13];\n```\n\nDetermine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.\n\nWrite a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "The following quantum circuit operates on 3 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncx q[2],q[0];\nrz(2.284789119577985) q[1];\ncx q[0],q[2];\nrz(6.231562207906491) q[0];\n```\n\nMap this circuit to a device with 5 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "The following quantum circuit operates on 3 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncx q[2],q[1];\ncx q[2],q[0];\n```\n\nMap this circuit to a device with 5 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "The following quantum circuit operates on 3 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncx q[2],q[0];\ncx q[2],q[1];\n```\n\nMap this circuit to a device with 5 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "The following quantum circuit operates on 3 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncx q[2],q[0];\ncx q[1],q[0];\nrz(2.282957393933801) q[1];\n```\n\nMap this circuit to a device with 5 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "The following quantum circuit operates on 3 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[3];\ncx q[2],q[0];\ncx q[0],q[2];\n```\n\nMap this circuit to a device with 5 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "The following quantum circuit operates on 4 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[0],q[2];\ncx q[0],q[2];\ncx q[2],q[1];\ncx q[1],q[0];\ncx q[3],q[1];\nrz(4.5399399394392095) q[0];\n```\n\nMap this circuit to a device with 6 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "The following quantum circuit operates on 4 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[3],q[1];\ncx q[3],q[0];\nrz(4.36559303510342) q[1];\ncx q[1],q[0];\ncx q[0],q[3];\ncx q[3],q[0];\n```\n\nMap this circuit to a device with 6 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "The following quantum circuit operates on 4 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[3],q[1];\ncx q[1],q[3];\nrz(3.795291598684939) q[2];\ncx q[1],q[3];\ncx q[3],q[0];\ncx q[1],q[3];\nrz(4.587769480680755) q[1];\n```\n\nMap this circuit to a device with 6 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "The following quantum circuit operates on 4 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[0],q[2];\nrz(3.9226505986372455) q[2];\ncx q[1],q[3];\nrz(4.498088868271407) q[3];\ncx q[2],q[0];\ncx q[2],q[1];\nrz(3.318174983115968) q[0];\ncx q[0],q[1];\nrz(5.1810652839065146) q[1];\n```\n\nMap this circuit to a device with 6 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "The following quantum circuit operates on 4 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[4];\ncx q[0],q[1];\ncx q[0],q[1];\ncx q[1],q[2];\ncx q[0],q[3];\ncx q[1],q[2];\n```\n\nMap this circuit to a device with 6 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "The following quantum circuit operates on 5 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\ncx q[1],q[3];\ncx q[3],q[2];\ncx q[4],q[1];\nrz(1.5349439970466117) q[0];\ncx q[0],q[4];\ncx q[4],q[1];\ncx q[3],q[4];\ncx q[3],q[2];\ncx q[1],q[2];\n```\n\nMap this circuit to a device with 7 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "The following quantum circuit operates on 5 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\ncx q[3],q[1];\ncx q[3],q[0];\ncx q[4],q[2];\ncx q[4],q[0];\ncx q[2],q[0];\nrz(5.351157746381014) q[4];\ncx q[1],q[4];\ncx q[0],q[2];\nrz(2.3698183379520237) q[2];\ncx q[2],q[3];\n```\n\nMap this circuit to a device with 7 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "The following quantum circuit operates on 5 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\ncx q[0],q[4];\nrz(1.735827999833344) q[3];\ncx q[3],q[4];\ncx q[4],q[2];\ncx q[0],q[3];\ncx q[0],q[1];\nrz(5.727811035769594) q[3];\ncx q[2],q[1];\ncx q[4],q[0];\ncx q[4],q[3];\nrz(0.23231044554829244) q[3];\n```\n\nMap this circuit to a device with 7 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "The following quantum circuit operates on 5 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\ncx q[0],q[4];\nrz(5.522406171766144) q[4];\ncx q[1],q[3];\ncx q[1],q[3];\ncx q[1],q[4];\ncx q[2],q[4];\ncx q[1],q[4];\nrz(3.0560856552576325) q[2];\ncx q[0],q[1];\nrz(4.996651422508294) q[0];\ncx q[4],q[2];\n```\n\nMap this circuit to a device with 7 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "The following quantum circuit operates on 5 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[5];\ncx q[2],q[1];\ncx q[1],q[3];\ncx q[3],q[1];\ncx q[0],q[3];\nrz(0.6309146082747762) q[0];\ncx q[3],q[0];\ncx q[2],q[4];\ncx q[4],q[1];\ncx q[1],q[3];\n```\n\nMap this circuit to a device with 7 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "The following quantum circuit operates on 7 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\ncx q[0],q[3];\ncx q[6],q[0];\ncx q[6],q[1];\ncx q[0],q[2];\nrz(2.414735894460961) q[3];\ncx q[4],q[0];\ncx q[0],q[2];\nrz(0.41811569544635546) q[0];\ncx q[3],q[5];\nrz(3.1348290892704624) q[0];\ncx q[1],q[4];\nrz(2.3140264400830906) q[4];\ncx q[3],q[6];\ncx q[5],q[1];\ncx q[2],q[4];\nrz(0.42874143515397933) q[2];\ncx q[5],q[3];\n```\n\nMap this circuit to a device with 9 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "The following quantum circuit operates on 7 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\ncx q[5],q[4];\nrz(5.919715403701441) q[0];\ncx q[6],q[4];\nrz(6.191429131053792) q[6];\ncx q[1],q[6];\ncx q[1],q[6];\nrz(5.931891424771653) q[4];\ncx q[5],q[1];\ncx q[5],q[4];\ncx q[6],q[5];\nrz(3.231267583401835) q[5];\ncx q[3],q[5];\nrz(3.9609828642098486) q[2];\ncx q[6],q[0];\nrz(4.727754342911764) q[4];\ncx q[3],q[2];\ncx q[5],q[3];\nrz(4.7463874224956655) q[2];\ncx q[0],q[2];\nrz(4.981694506209259) q[6];\n```\n\nMap this circuit to a device with 9 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "The following quantum circuit operates on 7 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\ncx q[5],q[6];\nrz(6.104872221436945) q[2];\ncx q[5],q[6];\ncx q[0],q[6];\nrz(5.5834130220724845) q[6];\ncx q[5],q[3];\nrz(2.5310080093163614) q[4];\ncx q[1],q[0];\ncx q[1],q[5];\ncx q[5],q[2];\ncx q[2],q[0];\ncx q[5],q[0];\ncx q[1],q[0];\ncx q[4],q[2];\ncx q[1],q[6];\n```\n\nMap this circuit to a device with 9 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "The following quantum circuit operates on 7 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\ncx q[3],q[1];\ncx q[5],q[1];\nrz(3.521966798448869) q[1];\ncx q[1],q[2];\nrz(2.3634462525311553) q[6];\ncx q[6],q[3];\ncx q[3],q[6];\ncx q[1],q[2];\nrz(0.4283196418696909) q[3];\ncx q[5],q[1];\ncx q[4],q[2];\ncx q[6],q[4];\ncx q[6],q[2];\ncx q[4],q[5];\nrz(5.278910766928672) q[1];\ncx q[3],q[5];\n```\n\nMap this circuit to a device with 9 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "The following quantum circuit operates on 7 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[7];\ncx q[4],q[2];\nrz(2.6523190670871397) q[4];\ncx q[3],q[2];\nrz(3.562063793550325) q[4];\ncx q[2],q[6];\nrz(3.1764206838126356) q[6];\ncx q[0],q[6];\ncx q[0],q[5];\ncx q[6],q[1];\ncx q[1],q[0];\nrz(4.525343995271579) q[4];\ncx q[4],q[1];\ncx q[6],q[5];\nrz(0.265050513446331) q[5];\ncx q[0],q[3];\ncx q[0],q[5];\nrz(1.796947653432336) q[0];\ncx q[0],q[1];\n```\n\nMap this circuit to a device with 9 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "The following quantum circuit operates on 10 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ncx q[9],q[5];\nrz(5.022177120804256) q[8];\ncx q[8],q[9];\ncx q[1],q[2];\ncx q[6],q[8];\nrz(5.673081358880238) q[6];\ncx q[0],q[2];\ncx q[7],q[3];\nrz(1.726006211026131) q[3];\ncx q[5],q[7];\nrz(6.147431845307644) q[3];\ncx q[0],q[5];\ncx q[0],q[4];\nrz(4.598095134420014) q[5];\ncx q[6],q[5];\nrz(4.059661402883541) q[0];\ncx q[2],q[4];\ncx q[8],q[4];\nrz(1.7801064889693083) q[3];\ncx q[1],q[8];\nrz(2.9818211567871225) q[3];\ncx q[5],q[1];\nrz(3.077760183802101) q[2];\ncx q[9],q[0];\nrz(6.259996726195062) q[8];\ncx q[3],q[5];\ncx q[1],q[5];\ncx q[4],q[3];\nrz(4.213254482932426) q[8];\n```\n\nMap this circuit to a device with 12 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "The following quantum circuit operates on 10 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ncx q[8],q[9];\ncx q[5],q[3];\ncx q[8],q[9];\ncx q[5],q[1];\ncx q[5],q[4];\nrz(3.0763749920771226) q[4];\ncx q[3],q[2];\ncx q[6],q[4];\ncx q[8],q[1];\nrz(4.24316164988852) q[5];\ncx q[0],q[8];\ncx q[7],q[1];\nrz(2.225559308716508) q[1];\ncx q[4],q[9];\nrz(2.6036604343617165) q[1];\ncx q[9],q[3];\nrz(4.3145382906363015) q[6];\ncx q[2],q[6];\nrz(6.270055118642815) q[3];\ncx q[4],q[1];\nrz(0.026992685998655862) q[7];\ncx q[9],q[0];\ncx q[2],q[3];\ncx q[4],q[2];\ncx q[0],q[9];\n```\n\nMap this circuit to a device with 12 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "The following quantum circuit operates on 10 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ncx q[6],q[4];\nrz(5.903631994897631) q[1];\ncx q[9],q[4];\ncx q[2],q[1];\ncx q[4],q[9];\nrz(5.747657259314519) q[7];\ncx q[1],q[9];\ncx q[1],q[8];\ncx q[3],q[8];\ncx q[0],q[4];\ncx q[0],q[3];\ncx q[6],q[1];\nrz(1.4050438213885217) q[7];\ncx q[9],q[0];\ncx q[1],q[0];\ncx q[6],q[1];\ncx q[5],q[1];\nrz(2.057753015580604) q[7];\ncx q[4],q[6];\ncx q[6],q[9];\nrz(2.840368896821549) q[7];\ncx q[3],q[0];\nrz(5.17253891302812) q[4];\ncx q[4],q[5];\n```\n\nMap this circuit to a device with 12 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "The following quantum circuit operates on 10 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ncx q[9],q[1];\nrz(0.21851371773850076) q[9];\ncx q[3],q[0];\nrz(2.399006727514206) q[9];\ncx q[4],q[8];\ncx q[8],q[6];\nrz(6.116504181526717) q[1];\ncx q[6],q[9];\nrz(4.270364081620882) q[6];\ncx q[1],q[6];\nrz(4.107854540356539) q[9];\ncx q[8],q[1];\ncx q[3],q[9];\nrz(2.7976416542078946) q[8];\ncx q[2],q[0];\ncx q[8],q[9];\ncx q[6],q[0];\nrz(1.7224735541657494) q[4];\ncx q[0],q[7];\nrz(4.006509161932251) q[6];\ncx q[1],q[7];\ncx q[3],q[7];\nrz(0.3766765352450249) q[7];\ncx q[6],q[3];\nrz(1.8455765641641404) q[6];\ncx q[5],q[9];\ncx q[2],q[8];\nrz(3.7720322034224862) q[1];\ncx q[2],q[9];\nrz(3.290740753412172) q[7];\n```\n\nMap this circuit to a device with 12 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T8", "task_code": "C1_routing", "task_name": "Hardware Routing", "workflow_stage": "Compile", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "The following quantum circuit operates on 10 logical qubits:\n\n```\nOPENQASM 2.0;\ninclude \"qelib1.inc\";\nqreg q[10];\ncx q[4],q[6];\nrz(1.0849420259468958) q[7];\ncx q[1],q[8];\ncx q[4],q[8];\ncx q[8],q[6];\ncx q[9],q[8];\nrz(3.6008272129148207) q[1];\ncx q[1],q[4];\ncx q[0],q[3];\nrz(6.123269437251737) q[7];\ncx q[0],q[1];\nrz(3.431140520847325) q[2];\ncx q[5],q[9];\ncx q[3],q[8];\ncx q[9],q[5];\nrz(1.062109449312094) q[9];\ncx q[4],q[0];\ncx q[8],q[2];\ncx q[6],q[4];\ncx q[0],q[3];\ncx q[1],q[0];\ncx q[6],q[5];\nrz(0.32124003290525405) q[8];\ncx q[7],q[2];\n```\n\nMap this circuit to a device with 12 physical qubits and connectivity:\n[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]\n\nRequirements:\n- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.\n- The mapped circuit must be functionally equivalent to the original.\n- Minimize the number of inserted SWAPs.\n- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).\n- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).\n\nWrite a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00>.\n\nCircuit (4 gates applied in order):\n  t on qubits [0]\n  s on qubits [0]\n  cx on qubits [0, 1]\n  y on qubits [1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.01\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.05\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00>.\n\nCircuit (4 gates applied in order):\n  ry(0.150202) on qubits [1]\n  x on qubits [0]\n  s on qubits [1]\n  t on qubits [1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.01\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.05\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00>.\n\nCircuit (4 gates applied in order):\n  y on qubits [1]\n  cx on qubits [0, 1]\n  h on qubits [0]\n  ry(1.200757) on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.01\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.05\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00>.\n\nCircuit (4 gates applied in order):\n  h on qubits [0]\n  y on qubits [0]\n  x on qubits [0]\n  rz(4.223213) on qubits [1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.01\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.05\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00>.\n\nCircuit (4 gates applied in order):\n  cx on qubits [1, 0]\n  h on qubits [1]\n  s on qubits [1]\n  ry(1.337598) on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.01\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.05\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |000>.\n\nCircuit (8 gates applied in order):\n  cx on qubits [0, 2]\n  t on qubits [2]\n  y on qubits [0]\n  s on qubits [0]\n  cx on qubits [0, 2]\n  h on qubits [1]\n  rz(1.045059) on qubits [2]\n  ry(3.592956) on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.005\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.02\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |000>.\n\nCircuit (8 gates applied in order):\n  rx(0.642837) on qubits [2]\n  cx on qubits [1, 0]\n  s on qubits [0]\n  cx on qubits [1, 2]\n  cx on qubits [2, 1]\n  cx on qubits [2, 1]\n  h on qubits [1]\n  s on qubits [2]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.005\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.02\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |000>.\n\nCircuit (8 gates applied in order):\n  y on qubits [2]\n  ry(3.834888) on qubits [1]\n  x on qubits [0]\n  y on qubits [2]\n  cx on qubits [2, 0]\n  s on qubits [0]\n  h on qubits [2]\n  h on qubits [1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.005\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.02\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |000>.\n\nCircuit (8 gates applied in order):\n  x on qubits [0]\n  s on qubits [2]\n  cx on qubits [2, 1]\n  z on qubits [1]\n  cx on qubits [2, 0]\n  t on qubits [0]\n  t on qubits [2]\n  cx on qubits [0, 1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.005\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.02\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |000>.\n\nCircuit (8 gates applied in order):\n  ry(4.374501) on qubits [2]\n  s on qubits [0]\n  y on qubits [2]\n  ry(3.504125) on qubits [1]\n  s on qubits [1]\n  t on qubits [0]\n  x on qubits [1]\n  y on qubits [1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.005\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.02\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |0000>.\n\nCircuit (15 gates applied in order):\n  s on qubits [2]\n  x on qubits [1]\n  cx on qubits [0, 2]\n  cx on qubits [3, 0]\n  rz(6.136252) on qubits [1]\n  z on qubits [0]\n  t on qubits [0]\n  ry(1.381243) on qubits [1]\n  h on qubits [3]\n  x on qubits [1]\n  s on qubits [1]\n  y on qubits [1]\n  h on qubits [1]\n  x on qubits [1]\n  y on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.003\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.015\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |0000>.\n\nCircuit (15 gates applied in order):\n  z on qubits [1]\n  s on qubits [3]\n  cx on qubits [1, 0]\n  x on qubits [0]\n  cx on qubits [2, 3]\n  rx(5.926695) on qubits [3]\n  cx on qubits [2, 1]\n  y on qubits [3]\n  cx on qubits [1, 0]\n  z on qubits [2]\n  cx on qubits [1, 3]\n  z on qubits [2]\n  s on qubits [3]\n  rz(2.584050) on qubits [2]\n  cx on qubits [2, 3]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.003\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.015\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |0000>.\n\nCircuit (15 gates applied in order):\n  s on qubits [0]\n  cx on qubits [2, 3]\n  z on qubits [0]\n  cx on qubits [1, 2]\n  t on qubits [0]\n  y on qubits [2]\n  rx(3.743972) on qubits [3]\n  s on qubits [1]\n  cx on qubits [3, 1]\n  x on qubits [2]\n  rx(3.686055) on qubits [2]\n  x on qubits [0]\n  t on qubits [3]\n  s on qubits [0]\n  z on qubits [1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.003\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.015\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |0000>.\n\nCircuit (15 gates applied in order):\n  cx on qubits [1, 3]\n  x on qubits [2]\n  rz(5.119827) on qubits [0]\n  s on qubits [2]\n  t on qubits [3]\n  cx on qubits [0, 1]\n  cx on qubits [1, 0]\n  h on qubits [1]\n  h on qubits [0]\n  z on qubits [0]\n  x on qubits [1]\n  cx on qubits [2, 3]\n  cx on qubits [1, 2]\n  rx(3.599562) on qubits [0]\n  ry(3.196169) on qubits [3]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.003\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.015\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |0000>.\n\nCircuit (15 gates applied in order):\n  s on qubits [1]\n  y on qubits [2]\n  h on qubits [1]\n  rx(0.139009) on qubits [0]\n  t on qubits [1]\n  h on qubits [3]\n  rx(4.835409) on qubits [3]\n  z on qubits [2]\n  cx on qubits [3, 1]\n  cx on qubits [2, 0]\n  rz(2.768936) on qubits [0]\n  rz(0.243076) on qubits [3]\n  s on qubits [2]\n  z on qubits [3]\n  x on qubits [2]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.003\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.015\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (20 gates applied in order):\n  cx on qubits [1, 0]\n  cx on qubits [4, 2]\n  ry(6.012392) on qubits [4]\n  cx on qubits [0, 1]\n  y on qubits [2]\n  cx on qubits [4, 0]\n  cx on qubits [2, 4]\n  h on qubits [3]\n  rx(2.981315) on qubits [1]\n  y on qubits [0]\n  t on qubits [4]\n  cx on qubits [4, 1]\n  rz(4.481628) on qubits [3]\n  t on qubits [3]\n  x on qubits [0]\n  rz(5.843443) on qubits [2]\n  y on qubits [4]\n  cx on qubits [4, 2]\n  t on qubits [3]\n  cx on qubits [1, 2]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.002\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.01\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (20 gates applied in order):\n  rx(5.925500) on qubits [0]\n  z on qubits [1]\n  s on qubits [1]\n  x on qubits [1]\n  cx on qubits [1, 4]\n  y on qubits [0]\n  rz(6.208256) on qubits [3]\n  y on qubits [1]\n  cx on qubits [1, 0]\n  cx on qubits [0, 1]\n  z on qubits [3]\n  z on qubits [4]\n  rx(1.175447) on qubits [2]\n  t on qubits [1]\n  ry(6.008857) on qubits [0]\n  cx on qubits [0, 4]\n  s on qubits [4]\n  ry(2.850138) on qubits [4]\n  rx(5.692493) on qubits [1]\n  rx(5.301326) on qubits [4]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.002\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.01\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (20 gates applied in order):\n  h on qubits [1]\n  z on qubits [0]\n  s on qubits [1]\n  z on qubits [4]\n  cx on qubits [1, 2]\n  y on qubits [1]\n  s on qubits [1]\n  t on qubits [1]\n  t on qubits [1]\n  cx on qubits [4, 2]\n  rz(6.079493) on qubits [2]\n  s on qubits [2]\n  t on qubits [3]\n  cx on qubits [1, 0]\n  cx on qubits [1, 0]\n  cx on qubits [0, 2]\n  cx on qubits [4, 0]\n  cx on qubits [3, 1]\n  cx on qubits [4, 2]\n  cx on qubits [3, 4]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.002\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.01\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (20 gates applied in order):\n  cx on qubits [4, 3]\n  ry(3.565913) on qubits [1]\n  rx(2.425831) on qubits [4]\n  cx on qubits [2, 4]\n  s on qubits [4]\n  cx on qubits [1, 4]\n  cx on qubits [3, 0]\n  y on qubits [4]\n  h on qubits [2]\n  x on qubits [3]\n  x on qubits [2]\n  s on qubits [3]\n  cx on qubits [1, 2]\n  cx on qubits [3, 1]\n  y on qubits [1]\n  z on qubits [0]\n  s on qubits [0]\n  ry(2.901252) on qubits [3]\n  cx on qubits [3, 2]\n  rx(1.899734) on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.002\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.01\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (20 gates applied in order):\n  x on qubits [0]\n  t on qubits [3]\n  y on qubits [1]\n  rx(0.821224) on qubits [2]\n  h on qubits [1]\n  h on qubits [1]\n  z on qubits [1]\n  x on qubits [2]\n  x on qubits [3]\n  cx on qubits [1, 0]\n  h on qubits [0]\n  x on qubits [4]\n  cx on qubits [1, 4]\n  s on qubits [3]\n  t on qubits [3]\n  cx on qubits [1, 0]\n  cx on qubits [1, 2]\n  cx on qubits [2, 3]\n  x on qubits [2]\n  z on qubits [1]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.002\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.01\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (30 gates applied in order):\n  h on qubits [0]\n  z on qubits [0]\n  t on qubits [4]\n  t on qubits [0]\n  rz(5.024267) on qubits [4]\n  ry(1.798536) on qubits [4]\n  cx on qubits [4, 0]\n  h on qubits [0]\n  cx on qubits [1, 2]\n  cx on qubits [2, 3]\n  cx on qubits [3, 2]\n  rx(3.788735) on qubits [4]\n  ry(1.851775) on qubits [4]\n  cx on qubits [0, 3]\n  x on qubits [2]\n  cx on qubits [4, 0]\n  cx on qubits [2, 1]\n  ry(1.272514) on qubits [2]\n  z on qubits [1]\n  cx on qubits [2, 4]\n  ry(2.176526) on qubits [3]\n  x on qubits [2]\n  cx on qubits [4, 1]\n  y on qubits [1]\n  rx(2.362067) on qubits [0]\n  cx on qubits [3, 2]\n  s on qubits [0]\n  cx on qubits [3, 4]\n  s on qubits [4]\n  cx on qubits [4, 2]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.001\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.008\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (30 gates applied in order):\n  h on qubits [2]\n  cx on qubits [1, 3]\n  s on qubits [0]\n  t on qubits [2]\n  cx on qubits [4, 1]\n  s on qubits [2]\n  t on qubits [0]\n  ry(5.172327) on qubits [3]\n  x on qubits [3]\n  cx on qubits [2, 0]\n  y on qubits [0]\n  y on qubits [4]\n  y on qubits [3]\n  cx on qubits [1, 3]\n  h on qubits [0]\n  cx on qubits [0, 3]\n  ry(4.690190) on qubits [1]\n  x on qubits [0]\n  t on qubits [3]\n  z on qubits [1]\n  cx on qubits [3, 0]\n  cx on qubits [2, 3]\n  z on qubits [0]\n  s on qubits [1]\n  cx on qubits [2, 4]\n  rz(4.565329) on qubits [0]\n  z on qubits [3]\n  cx on qubits [2, 1]\n  s on qubits [1]\n  s on qubits [2]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.001\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.008\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (30 gates applied in order):\n  rx(5.909673) on qubits [1]\n  z on qubits [4]\n  y on qubits [2]\n  y on qubits [4]\n  rz(3.893760) on qubits [3]\n  h on qubits [0]\n  s on qubits [2]\n  t on qubits [3]\n  rz(1.482682) on qubits [0]\n  cx on qubits [4, 3]\n  h on qubits [0]\n  s on qubits [0]\n  s on qubits [3]\n  y on qubits [3]\n  cx on qubits [3, 2]\n  y on qubits [0]\n  y on qubits [2]\n  y on qubits [1]\n  y on qubits [3]\n  s on qubits [1]\n  rx(5.354935) on qubits [2]\n  s on qubits [0]\n  rx(2.171684) on qubits [0]\n  y on qubits [3]\n  s on qubits [4]\n  h on qubits [0]\n  rx(1.356998) on qubits [4]\n  t on qubits [4]\n  cx on qubits [4, 0]\n  rx(6.103324) on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.001\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.008\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (30 gates applied in order):\n  x on qubits [0]\n  cx on qubits [1, 0]\n  cx on qubits [4, 3]\n  t on qubits [3]\n  h on qubits [3]\n  s on qubits [1]\n  x on qubits [1]\n  cx on qubits [3, 4]\n  z on qubits [1]\n  t on qubits [1]\n  cx on qubits [1, 2]\n  z on qubits [3]\n  h on qubits [1]\n  cx on qubits [0, 3]\n  cx on qubits [2, 1]\n  cx on qubits [1, 0]\n  ry(0.470682) on qubits [3]\n  cx on qubits [4, 1]\n  rz(4.781103) on qubits [2]\n  cx on qubits [4, 0]\n  y on qubits [2]\n  cx on qubits [2, 4]\n  y on qubits [4]\n  cx on qubits [4, 2]\n  ry(6.231225) on qubits [3]\n  cx on qubits [3, 4]\n  rz(3.598171) on qubits [1]\n  rz(0.325366) on qubits [1]\n  t on qubits [2]\n  rz(2.144874) on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.001\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.008\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T9", "task_code": "I1_noise", "task_name": "Noise Fidelity", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "Given this 5-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.\n\nThe initial state is |00000>.\n\nCircuit (30 gates applied in order):\n  z on qubits [0]\n  cx on qubits [0, 3]\n  t on qubits [1]\n  s on qubits [4]\n  cx on qubits [4, 2]\n  x on qubits [0]\n  rx(2.532508) on qubits [3]\n  rx(2.122953) on qubits [1]\n  s on qubits [4]\n  t on qubits [3]\n  x on qubits [1]\n  cx on qubits [2, 0]\n  t on qubits [3]\n  rz(4.134292) on qubits [1]\n  ry(4.808796) on qubits [1]\n  cx on qubits [4, 2]\n  rx(5.057470) on qubits [3]\n  cx on qubits [1, 0]\n  rz(0.887469) on qubits [0]\n  t on qubits [1]\n  cx on qubits [1, 3]\n  x on qubits [0]\n  h on qubits [4]\n  h on qubits [4]\n  rx(1.479008) on qubits [4]\n  cx on qubits [4, 3]\n  cx on qubits [1, 2]\n  cx on qubits [2, 3]\n  cx on qubits [3, 2]\n  y on qubits [0]\n\nNoise model: depolarizing noise applied AFTER each gate.\n  - After each 1-qubit gate: depolarizing channel with probability p = 0.001\n    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)\n  - After each 2-qubit gate: depolarizing channel with probability p = 0.008\n    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\\II} P*rho*P\n    (sum over all 15 non-identity two-qubit Pauli operators)\n\nStandard gate definitions:\n  h: (1/sqrt(2))*[[1,1],[1,-1]]\n  x: [[0,1],[1,0]]\n  y: [[0,-i],[i,0]]\n  z: [[1,0],[0,-1]]\n  s: [[1,0],[0,i]]\n  t: [[1,0],[0,exp(i*pi/4)]]\n  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]\n  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]\n  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]\n  cx: CNOT (control, target) in computational basis\n\nMulti-qubit operators use Qiskit convention: qubit 0 is LEAST significant (rightmost in tensor product). E.g., for gate on qubit k in an n-qubit system, the full operator is I_{n-1} \u2297 ... \u2297 Gate_k \u2297 ... \u2297 I_0.\n\nWrite a function `solve()` that returns a float (the predicted fidelity).\nYou may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.\nImplement density matrix propagation from scratch.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  +0.388411 * XY\n  -0.409094 * ZX\n  -0.674678 * IX\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, -1.0838+0.0000j, +0.0000+0.0000j, +0.0000-0.3884j]\n  [-1.0838+0.0000j, +0.0000+0.0000j, +0.0000+0.3884j, +0.0000+0.0000j]\n  [+0.0000+0.0000j, +0.0000-0.3884j, +0.0000+0.0000j, -0.2656+0.0000j]\n  [+0.0000+0.3884j, +0.0000+0.0000j, -0.2656+0.0000j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  -0.749955 * ZY\n  -1.475643 * XY\n  +1.161125 * IY\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, +0.0000-0.4112j, +0.0000+0.0000j, +0.0000+1.4756j]\n  [+0.0000+0.4112j, +0.0000+0.0000j, +0.0000-1.4756j, +0.0000+0.0000j]\n  [+0.0000+0.0000j, +0.0000+1.4756j, +0.0000+0.0000j, +0.0000-1.9111j]\n  [+0.0000-1.4756j, +0.0000+0.0000j, +0.0000+1.9111j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  +0.714373 * XY\n  -0.762022 * XZ\n  -0.564435 * IY\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, +0.0000+0.5644j, -0.7620+0.0000j, +0.0000-0.7144j]\n  [+0.0000-0.5644j, +0.0000+0.0000j, +0.0000+0.7144j, +0.7620+0.0000j]\n  [-0.7620+0.0000j, +0.0000-0.7144j, +0.0000+0.0000j, +0.0000+0.5644j]\n  [+0.0000+0.7144j, +0.7620+0.0000j, +0.0000-0.5644j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  -0.593950 * XZ\n  -0.410438 * IX\n  -0.783413 * ZX\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, -1.1939+0.0000j, -0.5940+0.0000j, +0.0000+0.0000j]\n  [-1.1939+0.0000j, +0.0000+0.0000j, +0.0000+0.0000j, +0.5940+0.0000j]\n  [-0.5940+0.0000j, +0.0000+0.0000j, +0.0000+0.0000j, +0.3730+0.0000j]\n  [+0.0000+0.0000j, +0.5940+0.0000j, +0.3730+0.0000j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  -0.514985 * XI\n  +0.704079 * XZ\n  -0.337695 * IY\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, +0.0000+0.3377j, +0.1891+0.0000j, +0.0000+0.0000j]\n  [+0.0000-0.3377j, +0.0000+0.0000j, +0.0000+0.0000j, -1.2191+0.0000j]\n  [+0.1891+0.0000j, +0.0000+0.0000j, +0.0000+0.0000j, +0.0000+0.3377j]\n  [+0.0000+0.0000j, -1.2191+0.0000j, +0.0000-0.3377j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  +0.884021 * YI\n  -0.255594 * YZ\n  -0.490551 * XY\n  +1.300056 * YY\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, +0.0000+0.0000j, +0.0000-0.6284j, -1.3001+0.4906j]\n  [+0.0000+0.0000j, +0.0000+0.0000j, +1.3001-0.4906j, +0.0000-1.1396j]\n  [+0.0000+0.6284j, +1.3001+0.4906j, +0.0000+0.0000j, +0.0000+0.0000j]\n  [-1.3001-0.4906j, +0.0000+1.1396j, +0.0000+0.0000j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  -1.434602 * XZ\n  -1.154895 * ZI\n  +0.584417 * XX\n  +1.357592 * IZ\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.2027+0.0000j, +0.0000+0.0000j, -1.4346+0.0000j, +0.5844+0.0000j]\n  [+0.0000+0.0000j, -2.5125+0.0000j, +0.5844+0.0000j, +1.4346+0.0000j]\n  [-1.4346+0.0000j, +0.5844+0.0000j, +2.5125+0.0000j, +0.0000+0.0000j]\n  [+0.5844+0.0000j, +1.4346+0.0000j, +0.0000+0.0000j, -0.2027+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  -0.260668 * XX\n  +0.293711 * XZ\n  -0.355289 * ZI\n  +0.481189 * YY\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [-0.3553+0.0000j, +0.0000+0.0000j, +0.2937+0.0000j, -0.7419+0.0000j]\n  [+0.0000+0.0000j, -0.3553+0.0000j, +0.2205+0.0000j, -0.2937+0.0000j]\n  [+0.2937+0.0000j, +0.2205+0.0000j, +0.3553+0.0000j, +0.0000+0.0000j]\n  [-0.7419+0.0000j, -0.2937+0.0000j, +0.0000+0.0000j, +0.3553+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  +0.422994 * XY\n  +0.372928 * XI\n  +0.886131 * YZ\n  +0.357041 * ZY\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, +0.0000-0.3570j, +0.3729-0.8861j, +0.0000-0.4230j]\n  [+0.0000+0.3570j, +0.0000+0.0000j, +0.0000+0.4230j, +0.3729+0.8861j]\n  [+0.3729+0.8861j, +0.0000-0.4230j, +0.0000+0.0000j, +0.0000+0.3570j]\n  [+0.0000+0.4230j, +0.3729-0.8861j, +0.0000-0.3570j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 2-qubit Hamiltonian:\n\nH =\n  -0.625860 * IX\n  +0.573932 * XZ\n  +0.539464 * IY\n  -0.106120 * YI\n\nAs a matrix (rows/cols ordered |0...0> to |1...1>):\n  [+0.0000+0.0000j, -0.6259-0.5395j, +0.5739+0.1061j, +0.0000+0.0000j]\n  [-0.6259+0.5395j, +0.0000+0.0000j, +0.0000+0.0000j, -0.5739+0.1061j]\n  [+0.5739-0.1061j, +0.0000+0.0000j, +0.0000+0.0000j, -0.6259-0.5395j]\n  [+0.0000+0.0000j, -0.5739-0.1061j, -0.6259+0.5395j, +0.0000+0.0000j]\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nYou may use any method including exact diagonalization (numpy.linalg.eigvalsh).\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  +0.015416 * ZXX\n  +1.140945 * ZXY\n  -1.256270 * XXI\n  -1.197515 * IXI\n  -1.449543 * ZXI\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  -0.213029 * ZXZ\n  +0.877352 * ZIY\n  -0.219276 * YZI\n  +0.169288 * IIX\n  -0.667628 * IYI\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  -1.363655 * IZY\n  +1.156962 * YIX\n  -0.173752 * YYI\n  -0.998578 * YIY\n  -0.154202 * XXX\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  -0.650431 * IIY\n  +0.566400 * ZYZ\n  -0.612789 * YZI\n  +0.935554 * XIY\n  +1.435760 * ZYX\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  -0.279532 * YXY\n  +0.736335 * ZXX\n  +0.516231 * XYX\n  -0.525929 * ZIX\n  +1.252587 * IYI\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  +0.519877 * YIX\n  -0.120012 * IZI\n  +1.497830 * IZX\n  -0.814065 * IXZ\n  -0.294305 * XII\n  -1.363248 * XIZ\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  -1.156454 * ZZX\n  +1.417826 * IXZ\n  +1.456190 * IZY\n  +1.132992 * YXX\n  -0.866199 * XXX\n  +0.819999 * XZZ\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  -0.623035 * ZZY\n  +0.870990 * XXZ\n  +1.432003 * YII\n  +1.001697 * ZZX\n  -0.733213 * IZY\n  -0.291533 * ZYI\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  +0.482597 * YXZ\n  -1.139532 * ZIY\n  -0.805483 * YXY\n  -0.974966 * ZYZ\n  +1.458830 * XZY\n  -1.105548 * ZXZ\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 3-qubit Hamiltonian:\n\nH =\n  -0.921306 * XYX\n  -0.219193 * YIX\n  +0.200760 * ZYX\n  +1.393010 * XXX\n  +1.386273 * YII\n  +1.349850 * IZI\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 4-qubit Hamiltonian:\n\nH =\n  -1.491903 * YZXZ\n  -1.059814 * YZZZ\n  +1.467246 * YXIY\n  -1.313575 * ZYIY\n  +1.096421 * XZII\n  -0.798604 * IZXZ\n  -1.369385 * XZXX\n  +1.435182 * IIXI\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 4-qubit Hamiltonian:\n\nH =\n  +0.264250 * ZZYX\n  +0.947579 * YIXY\n  +1.019813 * YYZZ\n  -0.145668 * YXYX\n  -0.582846 * ZIIX\n  +0.176328 * IYYX\n  +0.011389 * YXZI\n  +0.961026 * XIYY\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 4-qubit Hamiltonian:\n\nH =\n  -0.514446 * ZXYI\n  -0.528649 * XZYZ\n  +0.914676 * YZIZ\n  -0.334168 * XXZY\n  -0.979045 * XZIZ\n  +0.225206 * YYZY\n  +0.353006 * ZXII\n  -0.343815 * XYZY\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 4-qubit Hamiltonian:\n\nH =\n  -1.007755 * IZIZ\n  +1.404643 * YIIX\n  -0.145175 * IIZX\n  +0.992688 * XZZY\n  +1.420416 * IXIY\n  +0.715544 * YZZX\n  -1.103182 * XYIX\n  +0.258612 * ZZZY\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T10", "task_code": "E2_vqe", "task_name": "VQE", "workflow_stage": "Simulate", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "Find the ground state energy (lowest eigenvalue) of the following 4-qubit Hamiltonian:\n\nH =\n  -1.194971 * XYZY\n  +1.240787 * ZIZI\n  +0.843209 * ZYXX\n  +0.075903 * ZYYZ\n  +0.143694 * ZIYI\n  +0.584805 * IYII\n  -0.319779 * XIIZ\n  -0.890422 * XZII\n\nPauli string convention: rightmost character acts on qubit 0.\nExample: 'ZI' = Z on qubit 1, I on qubit 0.\n\nUse a variational quantum eigensolver (VQE) approach:\n  1. Define a parametrized ansatz circuit.\n  2. Compute E(\u03b8) = <\u03c8(\u03b8)|H|\u03c8(\u03b8)> using Qiskit's Estimator or by hand.\n  3. Minimize E(\u03b8) over \u03b8 with scipy.optimize.minimize.\nDo NOT use numpy.linalg.eig, scipy.linalg.eigh, or any exact diagonalization.\n\nWrite a function `solve()` that returns the ground state energy as a float.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 1, "difficulty": "Textbook", "seed": 1, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.01).\n\nSyndrome (24 detector bits):\n000000000100000010001000\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 1, "difficulty": "Textbook", "seed": 2, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.01).\n\nSyndrome (24 detector bits):\n000000100000011000000000\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 1, "difficulty": "Textbook", "seed": 3, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.01).\n\nSyndrome (24 detector bits):\n000010000001100000010000\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 1, "difficulty": "Textbook", "seed": 4, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.01).\n\nSyndrome (24 detector bits):\n000001000000000000000011\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 1, "difficulty": "Textbook", "seed": 5, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.01).\n\nSyndrome (24 detector bits):\n000000000100000001000000\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 2, "difficulty": "Homework", "seed": 1, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.02).\n\nSyndrome (24 detector bits):\n000000100001001000010010\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 2, "difficulty": "Homework", "seed": 2, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.02).\n\nSyndrome (24 detector bits):\n000000100100011000001000\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 2, "difficulty": "Homework", "seed": 3, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.02).\n\nSyndrome (24 detector bits):\n000010000000100000000000\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 2, "difficulty": "Homework", "seed": 4, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.02).\n\nSyndrome (24 detector bits):\n000000100000100000101110\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 2, "difficulty": "Homework", "seed": 5, "prompt": "You are given syndrome measurements from a distance-3 rotated surface code under circuit-level depolarizing noise (p=0.02).\n\nSyndrome (24 detector bits):\n011001001100000010000010\n\nThe syndrome was collected over 3 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 3, "difficulty": "Exam", "seed": 1, "prompt": "You are given syndrome measurements from a distance-5 rotated surface code under circuit-level depolarizing noise (p=0.005).\n\nSyndrome (120 detector bits):\n000000000010000000100000000000000000010000000000000000000000011000000000000000000000000000000000000000001000000000000010\n\nThe syndrome was collected over 5 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 3, "difficulty": "Exam", "seed": 2, "prompt": "You are given syndrome measurements from a distance-5 rotated surface code under circuit-level depolarizing noise (p=0.005).\n\nSyndrome (120 detector bits):\n000000000000000000000000000000000000000000000000000000000001000000000000000000000001000010000001000100000000000000111000\n\nThe syndrome was collected over 5 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 3, "difficulty": "Exam", "seed": 3, "prompt": "You are given syndrome measurements from a distance-5 rotated surface code under circuit-level depolarizing noise (p=0.005).\n\nSyndrome (120 detector bits):\n000010100000000000000000000000000000000000000000000000000000000000000000000000000000110010000010000001100000010011010000\n\nThe syndrome was collected over 5 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 3, "difficulty": "Exam", "seed": 4, "prompt": "You are given syndrome measurements from a distance-5 rotated surface code under circuit-level depolarizing noise (p=0.005).\n\nSyndrome (120 detector bits):\n000000000000000000010000000000000000000000010000000000000000000000000000000000000000101000000000000000000000000000000000\n\nThe syndrome was collected over 5 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 3, "difficulty": "Exam", "seed": 5, "prompt": "You are given syndrome measurements from a distance-5 rotated surface code under circuit-level depolarizing noise (p=0.005).\n\nSyndrome (120 detector bits):\n000000000000000000000000000000000000000000000000000000000000001000000000000000000000101000000000001000000000000001000000\n\nThe syndrome was collected over 5 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 4, "difficulty": "Research", "seed": 1, "prompt": "You are given syndrome measurements from a distance-7 rotated surface code under circuit-level depolarizing noise (p=0.007).\n\nSyndrome (336 detector bits):\n00000000000000000000000000000000010000000000000000000000000000000000000000000000100001000000000000000000000000000000000000000100000000000000000000000000000000000000000000001000000010000000000110001000... (336 total bits)\n\nThe syndrome was collected over 7 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 4, "difficulty": "Research", "seed": 2, "prompt": "You are given syndrome measurements from a distance-7 rotated surface code under circuit-level depolarizing noise (p=0.007).\n\nSyndrome (336 detector bits):\n00000100000000000000000000000001000000100001100000000101000000000000000000100000000000000000100000000100000000000000000000000000000000000000100000101000000100000000100100000000000000000000000010100000... (336 total bits)\n\nThe syndrome was collected over 7 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 4, "difficulty": "Research", "seed": 3, "prompt": "You are given syndrome measurements from a distance-7 rotated surface code under circuit-level depolarizing noise (p=0.007).\n\nSyndrome (336 detector bits):\n00000000000000000000000000000000000000000000000001000000000000000000000000000000000000000000010001001000100000000000000010000000000000000000000010100001000000000000000010000000000001001000000010100001... (336 total bits)\n\nThe syndrome was collected over 7 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 4, "difficulty": "Research", "seed": 4, "prompt": "You are given syndrome measurements from a distance-7 rotated surface code under circuit-level depolarizing noise (p=0.007).\n\nSyndrome (336 detector bits):\n00000000000000000000000000000000000100000010110000000100000010100000000000000000000000100010100000000000000000100001000000000011000000000000000000000000000100000001000000100000000000000000000001000000... (336 total bits)\n\nThe syndrome was collected over 7 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 4, "difficulty": "Research", "seed": 5, "prompt": "You are given syndrome measurements from a distance-7 rotated surface code under circuit-level depolarizing noise (p=0.007).\n\nSyndrome (336 detector bits):\n00000010010100000000100100011000000000000000000000000000010000000000000000011000000000000000110000001101000010000000000000010000000000000000100001000100000000100000000000010100000000000000001000000000... (336 total bits)\n\nThe syndrome was collected over 7 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 5, "difficulty": "Open", "seed": 1, "prompt": "You are given syndrome measurements from a distance-9 rotated surface code under circuit-level depolarizing noise (p=0.008).\n\nSyndrome (720 detector bits):\n00010000000000000000000011000000000000000000000000010000011000000000000000010110000001100000000100000000000100000000000000000000000000000000000110000000000000000000000000000000000000000000000001000000... (720 total bits)\n\nThe syndrome was collected over 9 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 5, "difficulty": "Open", "seed": 2, "prompt": "You are given syndrome measurements from a distance-9 rotated surface code under circuit-level depolarizing noise (p=0.008).\n\nSyndrome (720 detector bits):\n00000000000110110000000000000100000000000100000100010000001100000000100001100000000000110000001011010010000001000000000000100101010000000001000000001000001000000000000000000110100000010000000010000000... (720 total bits)\n\nThe syndrome was collected over 9 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 5, "difficulty": "Open", "seed": 3, "prompt": "You are given syndrome measurements from a distance-9 rotated surface code under circuit-level depolarizing noise (p=0.008).\n\nSyndrome (720 detector bits):\n00000000000100000000010010001000000000000011000001100000000000000000000010000000000000000000000000000000000001000110001000100000000000010000001100000000110000000110000000100000000000000100100001100000... (720 total bits)\n\nThe syndrome was collected over 9 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 5, "difficulty": "Open", "seed": 4, "prompt": "You are given syndrome measurements from a distance-9 rotated surface code under circuit-level depolarizing noise (p=0.008).\n\nSyndrome (720 detector bits):\n00000000000100100000001000100001000000000000000000000100000000000000100001010000000000000000000000001000100000000000000000000000001001011100010110000000000110000000000000000000000010001000001001000010... (720 total bits)\n\nThe syndrome was collected over 9 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}
{"task_id": "T11", "task_code": "D1_qec", "task_name": "QEC Decoding", "workflow_stage": "Error Correction", "level": 5, "difficulty": "Open", "seed": 5, "prompt": "You are given syndrome measurements from a distance-9 rotated surface code under circuit-level depolarizing noise (p=0.008).\n\nSyndrome (720 detector bits):\n00000000000000000010000000100000010001000001000000100000000100000000010000000000011000000001010101010000000000000001000100011000000000000001000000011000010000000100001000000000000000000100000000110010... (720 total bits)\n\nThe syndrome was collected over 9 rounds of stabilizer measurement.\n\nDetermine whether a logical X flip occurred on the data qubits.\n\nWrite a function `solve()` that returns True if a logical correction (X_L) is needed, or False if no correction is needed.\n"}