Prompt:
Analyze the following 7-qubit quantum circuit and identify what algorithm or subroutine it implements.

Circuit (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
u2(0,pi) q[0];
u3(pi,0,pi) q[0];
u2(0,pi) q[1];
u3(pi,0,pi) q[1];
u2(0,pi) q[2];
u3(pi,0,pi) q[2];
u2(0,pi) q[3];
u3(pi,0,pi) q[3];
u2(0,pi) q[4];
u3(pi,0,pi) q[4];
u2(0,pi) q[4];
cx q[3],q[4];
u3(0,0,-pi/4) q[4];
u2(0,pi) q[5];
u3(pi,0,pi) q[5];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
cx q[3],q[4];
u3(0,0,pi/4) q[3];
u3(0,0,-pi/4) q[4];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
u2(0,pi) q[4];
cx q[5],q[3];
u3(0,0,-pi/4) q[3];
u3(0,0,pi/4) q[5];
cx q[5],q[3];
cx q[5],q[3];
u3(pi,0,pi) q[5];
u3(pi,0,pi) q[5];
cx q[5],q[3];
cx q[5],q[4];
u2(0,pi) q[4];
cx q[3],q[4];
u3(0,0,-pi/4) q[4];
u2(0,pi) q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
u2(0,pi) q[5];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
cx q[3],q[4];
u3(0,0,pi/4) q[3];
u3(0,0,-pi/4) q[4];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
u2(0,pi) q[4];
cx q[5],q[3];
u3(0,0,-pi/4) q[3];
u3(0,0,pi/4) q[5];
cx q[5],q[3];
cx q[5],q[3];
u3(pi,0,pi) q[5];
u3(pi,0,pi) q[5];
u2(0,pi) q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u2(0,pi) q[2];
cx q[1],q[2];
u3(0,0,-pi/4) q[2];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
cx q[0],q[2];
u3(0,0,pi/4) q[2];
cx q[1],q[2];
u3(0,0,pi/4) q[1];
u3(0,0,-pi/4) q[2];
cx q[0],q[2];
cx q[0],q[1];
u3(0,0,pi/4) q[0];
u3(0,0,-pi/4) q[1];
cx q[0],q[1];
cx q[0],q[1];
u3(pi,0,pi) q[0];
u3(pi,0,pi) q[0];
u3(0,0,pi/4) q[2];
u2(0,pi) q[2];
u2(0,pi) q[5];
cx q[5],q[3];
cx q[5],q[4];
u2(0,pi) q[6];
u3(pi,0,pi) q[6];
u2(0,pi) q[6];
u2(0,pi) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[5];
cx q[4],q[5];
u3(0,0,pi/8) q[5];
cx q[4],q[5];
u3(pi,0,pi) q[4];
u2(0,pi) q[4];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/16) q[6];
cx q[5],q[6];
u3(0,0,-pi/16) q[6];
cx q[3],q[6];
u3(0,0,-pi/16) q[3];
u3(0,0,pi/16) q[6];
cx q[5],q[6];
u3(0,0,-pi/16) q[5];
cx q[3],q[5];
u3(0,0,pi/16) q[5];
cx q[3],q[5];
u3(pi,0,pi) q[3];
cx q[3],q[4];
u3(0,0,-pi/4) q[4];
u3(0,0,-pi/16) q[6];
cx q[2],q[6];
u3(0,0,pi/32) q[6];
cx q[5],q[6];
u3(0,0,-pi/32) q[6];
cx q[2],q[6];
u3(0,0,-pi/32) q[2];
u3(0,0,pi/32) q[6];
cx q[5],q[6];
u3(0,0,-pi/32) q[5];
cx q[2],q[5];
u3(0,0,pi/32) q[5];
cx q[2],q[5];
u3(pi,0,pi) q[2];
u3(0,0,-pi/32) q[6];
cx q[1],q[6];
u3(0,0,pi/64) q[6];
cx q[5],q[6];
u3(0,0,-pi/64) q[6];
cx q[1],q[6];
u3(0,0,-pi/64) q[1];
u3(0,0,pi/64) q[6];
cx q[5],q[6];
u3(0,0,-pi/64) q[5];
cx q[1],q[5];
u3(0,0,pi/64) q[5];
cx q[1],q[5];
u3(pi,0,pi) q[1];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
cx q[3],q[4];
u3(0,0,pi/4) q[3];
u3(0,0,-pi/4) q[4];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
u2(0,pi) q[4];
cx q[5],q[3];
u3(0,0,-pi/4) q[3];
u3(0,0,pi/4) q[5];
cx q[5],q[3];
cx q[5],q[3];
u3(pi,0,pi) q[5];
u3(pi,0,pi) q[5];
cx q[5],q[3];
cx q[5],q[4];
u2(0,pi) q[4];
cx q[3],q[4];
u3(0,0,-pi/4) q[4];
u2(0,pi) q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
u2(0,pi) q[5];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
cx q[3],q[4];
u3(0,0,pi/4) q[3];
u3(0,0,-pi/4) q[4];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
u2(0,pi) q[4];
cx q[5],q[3];
u3(0,0,-pi/4) q[3];
u3(0,0,pi/4) q[5];
cx q[5],q[3];
cx q[5],q[3];
u3(pi,0,pi) q[5];
u3(pi,0,pi) q[5];
u2(0,pi) q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u3(0,0,-pi/8) q[5];
cx q[1],q[5];
u3(0,0,pi/8) q[5];
cx q[2],q[5];
u2(0,pi) q[2];
cx q[1],q[2];
u3(0,0,-pi/4) q[2];
u3(0,0,-pi/8) q[5];
cx q[0],q[5];
cx q[0],q[2];
u3(0,0,pi/4) q[2];
cx q[1],q[2];
u3(0,0,pi/4) q[1];
u3(0,0,-pi/4) q[2];
cx q[0],q[2];
cx q[0],q[1];
u3(0,0,pi/4) q[0];
u3(0,0,-pi/4) q[1];
cx q[0],q[1];
cx q[0],q[1];
u3(pi,0,pi) q[0];
u3(pi,0,pi) q[0];
u3(pi,0,pi) q[1];
u3(0,0,pi/4) q[2];
u2(0,pi) q[2];
u3(pi,0,pi) q[2];
u2(0,pi) q[5];
cx q[5],q[3];
u3(pi,0,pi) q[3];
cx q[5],q[4];
u3(pi,0,pi) q[4];
u3(0,0,-pi/64) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
cx q[4],q[5];
u3(0,0,-pi/8) q[5];
cx q[4],q[5];
u3(pi,0,pi) q[4];
u2(0,pi) q[4];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/16) q[6];
cx q[5],q[6];
u3(0,0,pi/16) q[6];
cx q[3],q[6];
u3(0,0,pi/16) q[3];
u3(0,0,-pi/16) q[6];
cx q[5],q[6];
u3(0,0,pi/16) q[5];
cx q[3],q[5];
u3(0,0,-pi/16) q[5];
cx q[3],q[5];
u3(pi,0,pi) q[3];
u2(0,pi) q[3];
u3(0,0,pi/16) q[6];
cx q[2],q[6];
u3(0,0,-pi/32) q[6];
cx q[5],q[6];
u3(0,0,pi/32) q[6];
cx q[2],q[6];
u3(0,0,pi/32) q[2];
u3(0,0,-pi/32) q[6];
cx q[5],q[6];
u3(0,0,pi/32) q[5];
cx q[2],q[5];
u3(0,0,-pi/32) q[5];
cx q[2],q[5];
u3(pi,0,pi) q[2];
u2(0,pi) q[2];
u3(0,0,pi/32) q[6];
cx q[1],q[6];
u3(0,0,-pi/64) q[6];
cx q[5],q[6];
u3(0,0,pi/64) q[6];
cx q[1],q[6];
u3(0,0,pi/64) q[1];
u3(0,0,-pi/64) q[6];
cx q[5],q[6];
u3(0,0,pi/64) q[5];
cx q[1],q[5];
u3(0,0,-pi/64) q[5];
cx q[1],q[5];
u3(pi,0,pi) q[1];
u2(0,pi) q[1];
u3(0,0,pi/64) q[6];
cx q[0],q[6];
u3(0,0,-pi/64) q[6];
cx q[5],q[6];
u3(0,0,pi/64) q[6];
cx q[0],q[6];
u3(0,0,pi/64) q[0];
u3(0,0,-pi/64) q[6];
cx q[5],q[6];
u3(0,0,pi/64) q[5];
cx q[0],q[5];
u3(0,0,-pi/64) q[5];
cx q[0],q[5];
u3(pi,0,pi) q[0];
u2(0,pi) q[0];
u3(pi,0,pi) q[5];
u2(0,pi) q[5];
u3(0,0,pi/64) q[6];
u2(0,pi) q[6];
u2(0,pi) q[6];
u3(pi,0,pi) q[6];
u2(0,pi) q[6];
```

Write a function `solve()` that returns a dictionary with:
  - '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')
  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)

Valid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']


Prompt:
Analyze the following 7-qubit quantum circuit and identify what algorithm or subroutine it implements.

Circuit (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
u2(0,pi) q[0];
u2(0,pi) q[0];
u2(0,pi) q[1];
u2(0,pi) q[1];
u2(0,pi) q[2];
u2(0,pi) q[3];
u2(0,pi) q[3];
u2(0,pi) q[4];
u2(0,pi) q[4];
u2(0,pi) q[5];
u3(pi,0,pi) q[6];
u2(0,pi) q[6];
cx q[2],q[6];
u2(0,pi) q[2];
cx q[5],q[6];
u2(0,pi) q[5];
```

Write a function `solve()` that returns a dictionary with:
  - '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')
  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)

Valid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']


Prompt:
Analyze the following 6-qubit quantum circuit and identify what algorithm or subroutine it implements.

Circuit (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
u2(0,pi) q[0];
u2(0,pi) q[1];
u2(0,pi) q[1];
u2(0,pi) q[2];
u2(0,pi) q[3];
u2(0,pi) q[3];
u2(0,pi) q[4];
u3(pi,0,pi) q[5];
u2(0,pi) q[5];
cx q[0],q[5];
u2(0,pi) q[0];
cx q[2],q[5];
u2(0,pi) q[2];
cx q[4],q[5];
u2(0,pi) q[4];
```

Write a function `solve()` that returns a dictionary with:
  - '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')
  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)

Valid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']


Prompt:
Analyze the following 7-qubit quantum circuit and identify what algorithm or subroutine it implements.

Circuit (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
u2(0,pi) q[0];
u3(0,0,pi/8) q[0];
u2(0,pi) q[1];
u3(0,0,pi/8) q[1];
u2(0,pi) q[2];
u3(0,0,pi/8) q[2];
u2(0,pi) q[3];
u3(0,0,pi/8) q[3];
u2(0,pi) q[4];
u3(0,0,pi/8) q[4];
u2(0,pi) q[5];
u3(0,0,pi/8) q[5];
u3(pi,0,pi) q[6];
cx q[0],q[6];
u3(0,0,-pi/8) q[6];
cx q[0],q[6];
u3(0,0,pi/8) q[6];
cx q[1],q[6];
u3(0,0,-pi/8) q[6];
cx q[1],q[6];
u3(0,0,pi/8) q[1];
u3(0,0,pi/8) q[6];
cx q[1],q[6];
u3(0,0,-pi/8) q[6];
cx q[1],q[6];
u3(0,0,pi/8) q[6];
cx q[2],q[6];
u3(0,0,-pi/8) q[6];
cx q[2],q[6];
u3(0,0,pi/8) q[2];
u3(0,0,pi/8) q[6];
cx q[2],q[6];
u3(0,0,-pi/8) q[6];
cx q[2],q[6];
u3(0,0,pi/8) q[2];
u3(0,0,pi/8) q[6];
cx q[2],q[6];
u3(0,0,-pi/8) q[6];
cx q[2],q[6];
u3(0,0,pi/8) q[2];
u3(0,0,pi/8) q[6];
cx q[2],q[6];
u3(0,0,-pi/8) q[6];
cx q[2],q[6];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/8) q[3];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/8) q[3];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/8) q[3];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/8) q[3];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/8) q[3];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/8) q[3];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
u3(0,0,pi/8) q[3];
u3(0,0,pi/8) q[6];
cx q[3],q[6];
u3(0,0,-pi/8) q[6];
cx q[3],q[6];
cx q[2],q[3];
cx q[3],q[2];
cx q[2],q[3];
u3(0,0,-pi/8) q[2];
u3(0,0,-pi/16) q[3];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
u3(0,0,pi/8) q[4];
u3(0,0,pi/8) q[6];
cx q[4],q[6];
u3(0,0,-pi/8) q[6];
cx q[4],q[6];
cx q[1],q[4];
cx q[4],q[1];
cx q[1],q[4];
u3(0,0,-pi/4) q[1];
u3(0,0,-pi/32) q[4];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
u3(0,0,pi/8) q[5];
u3(0,0,pi/8) q[6];
cx q[5],q[6];
u3(0,0,-pi/8) q[6];
cx q[5],q[6];
cx q[0],q[5];
cx q[5],q[0];
cx q[0],q[5];
u2(0,pi) q[0];
cx q[1],q[0];
u3(0,0,pi/4) q[0];
cx q[1],q[0];
u3(0,0,-pi/4) q[0];
u2(0,pi) q[1];
cx q[2],q[0];
u3(0,0,pi/8) q[0];
cx q[2],q[0];
u3(0,0,-pi/8) q[0];
u3(0,0,-pi/4) q[2];
cx q[2],q[1];
u3(0,0,pi/4) q[1];
cx q[2],q[1];
u3(0,0,-pi/4) q[1];
u2(0,pi) q[2];
cx q[3],q[0];
u3(0,0,pi/16) q[0];
cx q[3],q[0];
u3(0,0,-pi/16) q[0];
u3(0,0,-pi/8) q[3];
cx q[3],q[1];
u3(0,0,pi/8) q[1];
cx q[3],q[1];
u3(0,0,-pi/8) q[1];
u3(0,0,-pi/4) q[3];
cx q[3],q[2];
u3(0,0,pi/4) q[2];
cx q[3],q[2];
u3(0,0,-pi/4) q[2];
u2(0,pi) q[3];
cx q[4],q[0];
u3(0,0,pi/32) q[0];
cx q[4],q[0];
u3(0,0,-pi/32) q[0];
u3(0,0,-pi/16) q[4];
cx q[4],q[1];
u3(0,0,pi/16) q[1];
cx q[4],q[1];
u3(0,0,-pi/16) q[1];
u3(0,0,-pi/8) q[4];
cx q[4],q[2];
u3(0,0,pi/8) q[2];
cx q[4],q[2];
u3(0,0,-pi/8) q[2];
u3(0,0,-pi/4) q[4];
cx q[4],q[3];
u3(0,0,pi/4) q[3];
cx q[4],q[3];
u3(0,0,-pi/4) q[3];
u2(0,pi) q[4];
u3(0,0,-pi/64) q[5];
cx q[5],q[0];
u3(0,0,pi/64) q[0];
cx q[5],q[0];
u3(0,0,-pi/64) q[0];
u3(0,0,-pi/32) q[5];
cx q[5],q[1];
u3(0,0,pi/32) q[1];
cx q[5],q[1];
u3(0,0,-pi/32) q[1];
u3(0,0,-pi/16) q[5];
cx q[5],q[2];
u3(0,0,pi/16) q[2];
cx q[5],q[2];
u3(0,0,-pi/16) q[2];
u3(0,0,-pi/8) q[5];
cx q[5],q[3];
u3(0,0,pi/8) q[3];
cx q[5],q[3];
u3(0,0,-pi/8) q[3];
u3(0,0,-pi/4) q[5];
cx q[5],q[4];
u3(0,0,pi/4) q[4];
cx q[5],q[4];
u3(0,0,-pi/4) q[4];
u2(0,pi) q[5];
u3(0,0,pi/8) q[6];
```

Write a function `solve()` that returns a dictionary with:
  - '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')
  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)

Valid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']


Prompt:
Analyze the following 6-qubit quantum circuit and identify what algorithm or subroutine it implements.

Circuit (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
u2(0,pi) q[0];
u2(0,pi) q[0];
u2(0,pi) q[1];
u2(0,pi) q[1];
u2(0,pi) q[2];
u2(0,pi) q[2];
u2(0,pi) q[3];
u2(0,pi) q[3];
u2(0,pi) q[4];
u2(0,pi) q[4];
u3(pi,0,pi) q[5];
u2(0,pi) q[5];
u3(pi,0,pi) q[5];
```

Write a function `solve()` that returns a dictionary with:
  - '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')
  - 'output': the expected output/result when run on the all-zeros input state (describe as a string)

Valid algorithm names: ['qft', 'inverse_qft', 'ghz', 'bell', 'grover_diffusion', 'swap_test', 'teleportation', 'phase_estimation_core', 'bernstein_vazirani', 'deutsch_jozsa']


Prompt:
Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
t q[1];
s q[1];
cz q[2],q[3];
s q[1];
s q[2];
cz q[3],q[0];
rz(4.124196450638081) q[3];
rz(5.565039855165545) q[0];
s q[0];
cx q[0],q[1];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
t q[1];
s q[1];
cz q[2],q[3];
s q[1];
s q[2];
cz q[3],q[0];
rz(4.124196450638081) q[3];
rz(6.15661964562299) q[0];
s q[0];
cx q[0],q[1];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
ry(0.15020205251846416) q[2];
x q[1];
s q[2];
t q[3];
t q[1];
cx q[0],q[1];
x q[3];
s q[1];
z q[1];
cx q[1],q[0];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
ry(0.15020205251846416) q[2];
x q[1];
s q[2];
t q[3];
t q[1];
cx q[0],q[1];
x q[3];
s q[1];
z q[1];
cx q[1],q[0];
s q[3];
s q[3];
z q[3];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
y q[3];
cx q[2],q[1];
ry(1.5391012516365692) q[1];
ry(1.8903295557165234) q[2];
s q[0];
h q[0];
cz q[2],q[3];
z q[2];
x q[3];
t q[1];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
t q[3];
cx q[2],q[1];
ry(1.5391012516365692) q[1];
ry(1.8903295557165234) q[2];
s q[0];
h q[0];
cz q[2],q[3];
z q[2];
x q[3];
t q[1];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
h q[1];
y q[0];
x q[1];
rz(4.223213152883283) q[2];
rx(5.970381465087641) q[1];
z q[0];
z q[0];
y q[1];
ry(4.464956090633724) q[1];
cz q[0],q[1];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
h q[1];
y q[0];
x q[1];
rz(4.223213152883283) q[2];
rx(5.970381465087641) q[1];
z q[0];
z q[0];
y q[1];
ry(4.464956090633724) q[1];
cz q[0],q[1];
h q[3];
h q[3];
h q[2];
h q[2];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 4-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
cx q[0],q[1];
z q[1];
x q[2];
cz q[2],q[1];
t q[1];
cz q[1],q[0];
cx q[0],q[3];
y q[0];
ry(1.705047798632293) q[1];
y q[2];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
cx q[0],q[1];
z q[1];
x q[2];
cz q[2],q[1];
t q[1];
cz q[1],q[0];
cx q[0],q[3];
y q[0];
ry(2.0760527595901395) q[1];
y q[2];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
cx q[3],q[5];
t q[2];
h q[4];
x q[0];
cz q[3],q[2];
t q[5];
cz q[1],q[3];
ry(3.5929563116952115) q[0];
rz(3.4324964786593237) q[0];
s q[4];
cx q[4],q[1];
t q[2];
cx q[0],q[4];
rz(5.687740598132069) q[5];
y q[0];
rz(4.962966954193391) q[1];
cz q[1],q[3];
t q[3];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
cx q[3],q[5];
t q[2];
h q[4];
x q[0];
cz q[3],q[2];
t q[5];
cz q[1],q[3];
ry(3.5929563116952115) q[0];
rz(3.4324964786593237) q[0];
s q[4];
cx q[4],q[1];
t q[2];
cx q[0],q[4];
rz(5.687740598132069) q[5];
y q[0];
rz(5.3488148949898795) q[1];
cz q[1],q[3];
t q[3];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
rx(0.6428373601854076) q[4];
cx q[2],q[0];
h q[5];
cz q[0],q[3];
s q[0];
y q[4];
y q[5];
t q[1];
cz q[0],q[1];
cx q[1],q[2];
cx q[4],q[3];
t q[4];
cz q[2],q[0];
x q[3];
cz q[2],q[0];
cz q[3],q[0];
h q[0];
cx q[0],q[1];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
rx(0.6428373601854076) q[4];
cx q[2],q[0];
h q[5];
cz q[0],q[3];
s q[0];
y q[4];
y q[5];
t q[1];
cz q[0],q[1];
cx q[1],q[2];
cx q[4],q[3];
t q[4];
cz q[2],q[0];
x q[3];
cz q[2],q[0];
cz q[3],q[0];
h q[0];
cx q[0],q[1];
h q[2];
h q[2];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
y q[5];
ry(3.834887656844354) q[2];
x q[0];
y q[5];
cx q[4],q[2];
h q[0];
s q[0];
z q[0];
cz q[0],q[2];
x q[5];
cz q[1],q[2];
h q[2];
cz q[3],q[4];
h q[4];
t q[3];
x q[0];
rx(3.0398623580969213) q[1];
rx(5.597481013744184) q[1];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
y q[5];
ry(3.834887656844354) q[2];
x q[0];
y q[5];
cx q[4],q[2];
h q[0];
s q[0];
z q[0];
cz q[0],q[2];
x q[5];
cz q[1],q[2];
h q[2];
cz q[3],q[4];
h q[4];
h q[3];
x q[0];
rx(3.0398623580969213) q[1];
rx(5.597481013744184) q[1];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
x q[0];
s q[4];
cz q[3],q[1];
z q[2];
cx q[0],q[4];
ry(5.198606068864962) q[2];
rx(0.7036137925742918) q[3];
h q[0];
rz(0.12030840945657001) q[5];
x q[1];
s q[1];
y q[5];
y q[0];
y q[0];
rz(2.382861097058146) q[1];
cx q[0],q[5];
t q[4];
cx q[2],q[1];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
x q[0];
s q[4];
cz q[3],q[1];
z q[2];
cx q[0],q[4];
ry(5.198606068864962) q[2];
rx(0.7036137925742918) q[3];
h q[0];
rz(0.12030840945657001) q[5];
x q[1];
s q[1];
y q[5];
y q[0];
y q[0];
rz(2.382861097058146) q[1];
cx q[0],q[5];
t q[4];
cx q[2],q[1];
h q[2];
h q[2];
h q[0];
h q[0];
h q[3];
h q[3];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 6-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
ry(4.374501019211292) q[5];
s q[0];
y q[5];
ry(3.504125488335103) q[3];
s q[3];
t q[0];
x q[3];
y q[2];
cz q[4],q[0];
rz(0.28223736532698923) q[0];
cx q[2],q[4];
s q[4];
s q[3];
ry(0.590853250194255) q[5];
t q[1];
s q[4];
cz q[3],q[0];
t q[5];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[6];
ry(4.374501019211292) q[5];
s q[0];
y q[5];
ry(3.504125488335103) q[3];
s q[3];
t q[0];
x q[3];
y q[2];
cz q[4],q[0];
rz(0.28223736532698923) q[0];
cx q[2],q[4];
s q[4];
s q[3];
ry(0.590853250194255) q[5];
t q[1];
s q[4];
cz q[3],q[0];
rz(0.9534354917268888) q[3];
t q[5];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
s q[5];
x q[2];
cz q[3],q[0];
cz q[1],q[3];
cz q[4],q[9];
z q[0];
t q[0];
ry(1.381243078207626) q[2];
h q[7];
x q[2];
s q[2];
y q[4];
h q[2];
x q[4];
y q[0];
z q[6];
cz q[8],q[9];
rx(3.089994700024885) q[8];
cz q[9],q[0];
h q[3];
z q[6];
ry(1.1479538098857254) q[5];
y q[5];
z q[3];
y q[4];
rx(0.2307321825133641) q[6];
rz(0.47122629548655287) q[4];
cz q[8],q[6];
cx q[5],q[6];
h q[6];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
s q[5];
x q[2];
cz q[3],q[0];
cz q[1],q[3];
cz q[4],q[9];
z q[0];
t q[0];
ry(1.381243078207626) q[2];
h q[7];
x q[2];
s q[2];
y q[4];
h q[2];
x q[4];
y q[0];
z q[6];
cz q[8],q[9];
rx(3.089994700024885) q[8];
cz q[9],q[0];
h q[3];
s q[6];
ry(1.1479538098857254) q[5];
y q[5];
z q[3];
y q[4];
rx(0.2307321825133641) q[6];
rz(0.47122629548655287) q[4];
cz q[8],q[6];
cx q[5],q[6];
h q[6];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
z q[4];
s q[9];
cx q[1],q[3];
x q[9];
cz q[7],q[4];
cx q[7],q[5];
cx q[2],q[6];
t q[1];
cx q[2],q[3];
y q[1];
h q[9];
x q[7];
x q[6];
cz q[4],q[7];
cz q[5],q[1];
cx q[3],q[1];
rx(1.366671214571527) q[1];
z q[4];
cx q[6],q[7];
h q[8];
z q[1];
z q[0];
y q[5];
z q[0];
h q[2];
cz q[2],q[3];
y q[5];
x q[6];
z q[8];
cz q[6],q[0];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
z q[4];
s q[9];
cx q[1],q[3];
x q[9];
cz q[7],q[4];
cx q[7],q[5];
cx q[2],q[6];
t q[1];
cx q[2],q[3];
y q[1];
h q[9];
x q[7];
x q[6];
cz q[4],q[7];
cz q[5],q[1];
cx q[3],q[1];
rx(1.366671214571527) q[1];
z q[4];
cx q[6],q[7];
h q[8];
z q[1];
z q[0];
y q[5];
z q[0];
h q[2];
cz q[2],q[3];
y q[5];
x q[6];
z q[8];
cz q[6],q[0];
h q[0];
h q[0];
x q[9];
x q[9];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
s q[0];
cz q[7],q[5];
h q[7];
cx q[3],q[4];
rz(5.736650091825691) q[6];
x q[0];
s q[4];
s q[0];
cx q[2],q[4];
ry(1.0463845822067088) q[8];
cx q[5],q[2];
z q[9];
z q[4];
y q[7];
h q[9];
y q[5];
y q[5];
t q[3];
cx q[1],q[4];
z q[9];
z q[3];
rz(5.56552043588244) q[6];
rx(0.17981425537182835) q[9];
t q[6];
z q[2];
cz q[3],q[2];
ry(1.2165291867695998) q[9];
cz q[8],q[3];
cx q[6],q[7];
cx q[4],q[8];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
s q[0];
cz q[7],q[5];
h q[7];
cx q[3],q[4];
rz(5.736650091825691) q[6];
x q[0];
s q[4];
s q[0];
cx q[2],q[4];
ry(1.0463845822067088) q[8];
cx q[5],q[2];
z q[9];
z q[4];
y q[7];
h q[9];
z q[5];
y q[5];
t q[3];
cx q[1],q[4];
z q[9];
z q[3];
rz(5.56552043588244) q[6];
rx(0.17981425537182835) q[9];
t q[6];
z q[2];
cz q[3],q[2];
ry(1.2165291867695998) q[9];
cz q[8],q[3];
cx q[6],q[7];
cx q[4],q[8];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
cz q[5],q[7];
z q[8];
rx(5.119827056542912) q[7];
z q[9];
t q[4];
cx q[1],q[4];
cz q[0],q[5];
rx(5.9260388984972) q[6];
h q[6];
cz q[7],q[6];
rz(0.14113982523033736) q[6];
cx q[1],q[2];
cx q[4],q[9];
rz(3.196168710917012) q[9];
s q[4];
y q[4];
ry(5.274683918594714) q[1];
cx q[4],q[6];
h q[7];
cx q[3],q[9];
t q[3];
t q[8];
y q[1];
rx(2.902055727548061) q[2];
z q[4];
rz(3.920918573880772) q[7];
t q[2];
ry(0.3958564474050542) q[8];
ry(4.876942177709919) q[0];
cx q[8],q[4];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
cz q[5],q[7];
z q[8];
rx(5.119827056542912) q[7];
z q[9];
t q[4];
cx q[1],q[4];
cz q[0],q[5];
rx(5.9260388984972) q[6];
h q[6];
cz q[7],q[6];
rz(0.14113982523033736) q[6];
cx q[1],q[2];
cx q[4],q[9];
rz(3.196168710917012) q[9];
s q[4];
y q[4];
ry(5.274683918594714) q[1];
cx q[4],q[6];
h q[7];
cx q[3],q[9];
t q[3];
t q[8];
y q[1];
rx(2.902055727548061) q[2];
z q[4];
rz(3.920918573880772) q[7];
t q[2];
ry(0.3958564474050542) q[8];
ry(4.876942177709919) q[0];
cx q[8],q[4];
h q[0];
h q[0];
s q[4];
s q[4];
z q[4];
h q[5];
h q[5];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 10-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
s q[4];
y q[6];
h q[3];
rx(0.13900911153489012) q[1];
t q[4];
h q[8];
rx(4.835408776863877) q[7];
z q[7];
cz q[8],q[2];
cx q[7],q[4];
cz q[7],q[1];
rz(0.24307604970574218) q[8];
s q[6];
z q[7];
x q[6];
rx(4.394326520326433) q[9];
x q[4];
rx(2.9117432417950204) q[9];
x q[5];
rx(2.142969749756436) q[5];
cz q[6],q[8];
cx q[4],q[5];
t q[9];
rx(4.653306259731393) q[1];
h q[6];
y q[4];
x q[4];
cx q[3],q[2];
cx q[8],q[0];
s q[2];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
s q[4];
y q[6];
h q[3];
rx(0.13900911153489012) q[1];
t q[4];
h q[8];
rx(4.835408776863877) q[7];
z q[7];
cz q[8],q[2];
cx q[7],q[4];
cz q[7],q[1];
rz(0.24307604970574218) q[8];
s q[6];
z q[7];
x q[6];
rx(4.394326520326433) q[9];
x q[4];
rx(2.9117432417950204) q[9];
x q[5];
rx(2.142969749756436) q[5];
cz q[6],q[8];
cx q[4],q[5];
t q[9];
rx(4.653306259731393) q[1];
h q[6];
y q[4];
x q[4];
cx q[2],q[3];
cx q[8],q[0];
s q[2];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
cx q[0],q[10];
cz q[5],q[2];
cz q[10],q[4];
cx q[1],q[0];
y q[0];
cz q[6],q[4];
ry(3.1849367347398965) q[4];
cx q[1],q[6];
s q[10];
y q[6];
y q[2];
cz q[8],q[4];
y q[8];
x q[8];
rx(0.35962690705794126) q[6];
s q[5];
t q[0];
x q[6];
x q[1];
h q[5];
cz q[8],q[11];
x q[11];
z q[3];
rx(4.070412921493407) q[2];
t q[11];
cx q[0],q[6];
y q[0];
ry(2.5699231395662565) q[8];
z q[6];
t q[2];
h q[10];
cz q[1],q[7];
rz(5.6508062204013285) q[1];
cx q[6],q[1];
rx(0.4850419713763551) q[7];
cz q[4],q[2];
t q[1];
s q[8];
z q[5];
t q[6];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
h q[2];
rz(3.9856967221918107) q[3];
h q[4];
cx q[5],q[2];
rz(-0.9288202679036139) q[2];
rx(-3*pi/4) q[2];
rz(pi/2) q[5];
ry(-pi/2) q[5];
h q[7];
cx q[0],q[10];
cx q[1],q[0];
ry(pi) q[0];
rz(pi/4) q[0];
cx q[10],q[4];
cx q[6],q[4];
cx q[1],q[6];
x q[1];
cx q[1],q[7];
rz(5.6508062204013285) q[1];
ry(3.4311082471990075) q[4];
ry(pi) q[6];
rx(3.5012195606477343) q[6];
cx q[0],q[6];
ry(pi) q[0];
rz(5*pi/4) q[6];
cx q[6],q[1];
rz(pi/4) q[1];
h q[7];
rx(0.4850419713763551) q[7];
cx q[8],q[4];
h q[4];
cx q[4],q[2];
h q[2];
rz(-pi) q[8];
rz(pi/2) q[10];
h q[10];
h q[11];
cx q[8],q[11];
ry(2.5699231395662565) q[8];
rz(pi/2) q[8];
ry(2.3079151298403477) q[11];
rz(pi/4) q[11];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
rx(5.92550020688181) q[1];
z q[2];
s q[3];
x q[3];
cx q[9],q[10];
x q[10];
ry(6.208256068892496) q[4];
x q[3];
cx q[1],q[6];
cz q[6],q[3];
z q[8];
ry(0.19199770660329826) q[9];
rz(4.713532602908841) q[9];
z q[3];
cz q[3],q[10];
x q[3];
s q[1];
h q[8];
cx q[4],q[2];
rx(5.301326267231974) q[9];
h q[7];
s q[6];
y q[4];
ry(1.9115838441514372) q[2];
cx q[0],q[4];
h q[0];
rx(3.057876950368099) q[5];
ry(5.859570670216837) q[3];
cx q[2],q[3];
cz q[4],q[3];
rz(2.2917904672326466) q[9];
cx q[8],q[9];
s q[2];
y q[6];
ry(3.7277276145540488) q[1];
cz q[5],q[8];
cx q[9],q[8];
y q[10];
x q[8];
s q[7];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
rx(5.92550020688181) q[1];
rz(pi) q[2];
rz(3*pi/2) q[3];
h q[3];
ry(6.208256068892496) q[4];
cx q[4],q[2];
ry(1.9115838441514372) q[2];
ry(pi) q[4];
cx q[0],q[4];
h q[0];
rx(3.057876950368099) q[5];
cx q[1],q[6];
rz(pi/2) q[1];
ry(3.7277276145540488) q[1];
cx q[6],q[3];
h q[3];
rz(pi/2) q[6];
ry(pi) q[6];
x q[0];
x q[0];
h q[7];
rz(pi/2) q[7];
ry(pi/2) q[8];
cx q[9],q[10];
rz(-3.1402537581828645) q[9];
ry(0.7898614794354343) q[9];
rz(-2.420905763480704) q[9];
x q[11];
x q[11];
cx q[8],q[9];
h q[8];
cx q[5],q[8];
h q[8];
cx q[9],q[8];
x q[8];
ry(-pi/2) q[10];
cx q[3],q[10];
x q[3];
ry(5.859570670216837) q[3];
cx q[2],q[3];
rz(pi/2) q[2];
h q[3];
cx q[4],q[3];
h q[3];
h q[10];
ry(pi) q[10];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
h q[3];
z q[1];
s q[3];
z q[11];
cz q[4],q[2];
x q[9];
y q[11];
x q[11];
y q[8];
cz q[8],q[5];
cz q[5],q[2];
s q[5];
t q[8];
cx q[5],q[3];
cx q[9],q[0];
cx q[7],q[1];
ry(4.69553845940479) q[9];
cz q[4],q[2];
y q[4];
cx q[10],q[6];
x q[0];
y q[0];
x q[5];
s q[0];
rz(4.7996101619797065) q[4];
rx(2.8433055314440168) q[4];
z q[0];
ry(2.9601008427458995) q[7];
cx q[0],q[2];
x q[2];
s q[9];
y q[6];
cx q[4],q[1];
z q[10];
t q[7];
s q[4];
rz(0.48415689123877803) q[5];
y q[9];
ry(1.089133865252038) q[0];
cx q[6],q[8];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
rz(pi) q[1];
h q[2];
h q[3];
rz(2.3347574695349964) q[3];
rz(-1.6580175083899134) q[4];
rx(-0.2982871221457766) q[4];
h q[5];
cx q[7],q[1];
cx q[4],q[1];
rz(pi/2) q[4];
ry(2.9601008427458995) q[7];
rz(pi/4) q[7];
ry(4.0781534851299766) q[8];
cx q[8],q[5];
h q[5];
cx q[5],q[2];
h q[2];
rz(pi/2) q[5];
cx q[5],q[3];
x q[5];
rz(0.48415689123877803) q[5];
rz(pi/4) q[8];
x q[9];
cx q[9],q[0];
rz(pi/2) q[0];
cx q[0],q[2];
ry(1.089133865252038) q[0];
x q[2];
ry(1.5539458058149966) q[9];
rz(-pi/2) q[9];
cx q[10],q[6];
ry(pi) q[6];
cx q[6],q[8];
rz(4.04943093227983) q[10];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
cz q[10],q[3];
rx(3.565912955911002) q[2];
rz(2.4258308371489203) q[6];
cz q[6],q[7];
x q[1];
h q[0];
y q[8];
z q[4];
x q[11];
t q[4];
s q[8];
rz(4.97320825750158) q[3];
cx q[10],q[4];
t q[6];
ry(3.5048648242575777) q[10];
cx q[6],q[4];
z q[1];
rz(1.9322388056630297) q[7];
cz q[3],q[6];
cx q[7],q[2];
cx q[7],q[5];
rx(2.8673857507137934) q[5];
x q[10];
cx q[10],q[4];
cx q[7],q[5];
z q[5];
t q[1];
cz q[6],q[4];
cz q[1],q[6];
h q[6];
h q[8];
cz q[7],q[11];
rx(3.6803672216376744) q[10];
h q[0];
h q[1];
cx q[2],q[1];
z q[3];
y q[10];
cx q[11],q[3];
cx q[10],q[11];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
x q[1];
rz(5*pi/4) q[1];
rx(3.565912955911002) q[2];
h q[3];
rz(5*pi/4) q[4];
rx(2.8673857507137934) q[5];
h q[8];
h q[8];
rz(pi) q[5];
rz(3.2112290005463686) q[6];
h q[7];
cx q[6],q[7];
h q[7];
rz(1.9322388056630297) q[7];
cx q[7],q[2];
rz(pi/2) q[8];
ry(-pi/2) q[8];
cx q[10],q[3];
h q[3];
rz(8.114800911091372) q[3];
cx q[10],q[4];
cx q[6],q[4];
h q[6];
cx q[3],q[6];
h q[6];
ry(3.5048648242575777) q[10];
x q[10];
cx q[10],q[4];
h q[4];
cx q[6],q[4];
h q[4];
h q[6];
cx q[1],q[6];
h q[1];
cx q[2],q[1];
rx(3.6803672216376744) q[10];
ry(pi) q[10];
ry(-pi/2) q[11];
cx q[7],q[11];
h q[11];
s q[1];
s q[1];
z q[1];
cx q[11],q[3];
cx q[10],q[11];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 12-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
x q[2];
t q[8];
y q[4];
rx(0.8212239749437135) q[6];
h q[2];
h q[3];
z q[3];
x q[6];
x q[9];
cx q[6],q[0];
h q[2];
t q[3];
cx q[9],q[4];
s q[7];
y q[3];
cz q[0],q[3];
ry(1.586927554328436) q[8];
y q[7];
y q[1];
s q[7];
ry(1.234869319072365) q[3];
cz q[6],q[2];
y q[4];
h q[6];
t q[2];
s q[1];
y q[9];
cx q[6],q[9];
z q[11];
h q[10];
h q[7];
cx q[10],q[7];
z q[6];
ry(5.520680537892614) q[6];
t q[1];
s q[6];
cz q[10],q[4];
s q[3];
cx q[10],q[6];
rx(3.6820866227845843) q[10];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[12];
rz(-3*pi/4) q[1];
ry(pi) q[1];
ry(-0.5868898936005222) q[2];
rz(-pi) q[3];
rx(-pi/4) q[3];
ry(pi) q[4];
rx(3.9628166285335067) q[6];
cx q[6],q[0];
cx q[0],q[3];
ry(-2.194550350678991) q[3];
rz(-pi/2) q[3];
cx q[6],q[2];
h q[2];
rz(pi/4) q[2];
h q[6];
rz(-pi) q[7];
ry(-0.574707481610585) q[7];
rz(pi/4) q[8];
ry(1.586927554328436) q[8];
x q[9];
cx q[9],q[4];
ry(pi) q[4];
h q[4];
ry(pi) q[9];
cx q[6],q[9];
ry(0.7625047692869729) q[6];
rz(-pi/2) q[6];
h q[10];
cx q[10],q[7];
cx q[10],q[4];
h q[4];
cx q[10],q[6];
rx(3.6820866227845843) q[10];
rz(pi) q[11];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
h q[0];
z q[2];
t q[13];
t q[0];
rz(5.024267334635643) q[12];
ry(1.798535968996919) q[11];
cx q[5],q[1];
h q[5];
cx q[11],q[6];
x q[1];
cz q[7],q[8];
y q[13];
cx q[9],q[12];
cz q[4],q[1];
y q[0];
cx q[0],q[6];
cz q[8],q[3];
cx q[13],q[7];
y q[9];
cz q[12],q[9];
cz q[11],q[8];
x q[5];
cx q[5],q[3];
y q[0];
rx(2.3620671057185727) q[8];
cz q[9],q[6];
ry(6.014813233512013) q[3];
z q[6];
ry(1.251801085655153) q[1];
rz(5.227142850173022) q[12];
ry(0.5892156730760137) q[7];
cz q[4],q[11];
cx q[3],q[4];
z q[6];
cz q[11],q[10];
ry(4.382101640568701) q[13];
cz q[8],q[7];
s q[12];
h q[4];
y q[8];
x q[0];
t q[5];
cz q[0],q[11];
t q[10];
t q[5];
cx q[6],q[11];
ry(3.128898118538559) q[5];
t q[6];
rz(5.904337709273202) q[12];
cz q[4],q[11];
x q[8];
y q[10];
rz(4.3730986066586315) q[3];
cz q[2],q[13];
y q[6];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
ry(2.3571585650319706) q[0];
rz(-pi/4) q[0];
rz(pi) q[2];
h q[3];
cx q[5],q[1];
ry(-0.7053085425866642) q[1];
cx q[4],q[1];
h q[1];
ry(1.251801085655153) q[1];
ry(pi/2) q[5];
h q[8];
cx q[7],q[8];
h q[8];
cx q[8],q[3];
h q[3];
cx q[5],q[3];
ry(6.014813233512013) q[3];
rz(pi/2) q[5];
ry(3.128898118538559) q[5];
h q[8];
rx(pi) q[9];
h q[10];
ry(1.798535968996919) q[11];
cx q[11],q[6];
cx q[0],q[6];
h q[6];
cx q[11],q[8];
h q[8];
rx(2.3620671057185727) q[8];
h q[11];
cx q[4],q[11];
cx q[3],q[4];
rz(4.3730986066586315) q[3];
h q[4];
h q[11];
cx q[11],q[10];
ry(2.0871287931858156) q[10];
rz(3*pi/4) q[10];
h q[11];
cx q[0],q[11];
h q[11];
rz(-2.829714299338839) q[12];
rx(-pi) q[12];
cx q[9],q[12];
rz(pi/2) q[9];
cx q[9],q[6];
h q[6];
cx q[6],q[11];
rz(pi/4) q[6];
ry(pi) q[6];
h q[11];
cx q[4],q[11];
h q[11];
rz(-1.4348900549129482) q[12];
rz(pi/4) q[13];
ry(pi) q[13];
cx q[13],q[7];
ry(0.5892156730760137) q[7];
h q[7];
cx q[8],q[7];
h q[7];
rz(-pi) q[8];
ry(4.382101640568701) q[13];
h q[13];
cx q[2],q[13];
h q[13];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
h q[8];
cx q[8],q[13];
x q[11];
z q[6];
cx q[4],q[6];
y q[7];
rz(1.0333545112402156) q[7];
s q[10];
t q[2];
t q[9];
x q[5];
z q[4];
y q[4];
x q[13];
cz q[11],q[0];
y q[3];
cx q[5],q[9];
t q[6];
z q[13];
z q[0];
rz(3.683410660595319) q[6];
h q[9];
x q[9];
cx q[9],q[2];
cz q[1],q[13];
z q[9];
cz q[3],q[8];
x q[9];
z q[0];
ry(4.041467099982676) q[7];
s q[0];
t q[9];
cx q[13],q[7];
cx q[8],q[6];
z q[0];
rx(1.0261827657685991) q[4];
cz q[2],q[13];
z q[1];
cx q[10],q[6];
cz q[4],q[3];
cz q[11],q[4];
z q[4];
x q[5];
cx q[1],q[12];
y q[4];
x q[5];
rx(2.3582214925279765) q[12];
cx q[2],q[0];
x q[2];
y q[7];
rz(1.3121359422204464) q[13];
cz q[8],q[6];
h q[11];
cx q[5],q[11];
cz q[3],q[10];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
h q[0];
rz(pi/4) q[2];
ry(pi) q[3];
x q[5];
rz(pi) q[6];
cx q[4],q[6];
s q[13];
s q[13];
z q[13];
rx(-2.115409887821194) q[4];
rz(4.4688088239927675) q[6];
rz(-1.0333545112402156) q[7];
ry(0.899874446392883) q[7];
h q[8];
rz(pi/4) q[9];
cx q[5],q[9];
ry(pi/2) q[9];
cx q[9],q[2];
rz(-pi/4) q[9];
s q[0];
s q[0];
z q[0];
ry(pi) q[9];
rz(pi/2) q[10];
x q[11];
cx q[11],q[0];
h q[8];
h q[8];
h q[0];
rz(3*pi/2) q[0];
cx q[8],q[13];
h q[8];
cx q[3],q[8];
h q[3];
cx q[4],q[3];
h q[3];
h q[4];
s q[10];
s q[10];
z q[10];
h q[8];
cx q[8],q[6];
cx q[10],q[6];
h q[6];
cx q[8],q[6];
h q[6];
h q[10];
cx q[3],q[10];
h q[10];
cx q[11],q[4];
ry(pi/2) q[4];
h q[11];
cx q[5],q[11];
rz(1.829456711369347) q[13];
ry(-pi/2) q[13];
cx q[1],q[13];
rz(pi) q[1];
cx q[1],q[12];
rx(2.3582214925279765) q[12];
h q[13];
cx q[13],q[7];
ry(pi) q[7];
h q[13];
cx q[2],q[13];
cx q[2],q[0];
x q[2];
h q[13];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
rx(5.909672773479288) q[4];
z q[12];
y q[5];
y q[12];
rz(3.893759820960499) q[9];
h q[1];
s q[7];
t q[9];
rz(1.4826818544450509) q[0];
cz q[1],q[8];
h q[9];
h q[10];
s q[6];
s q[8];
cz q[9],q[4];
ry(5.19021539939376) q[9];
s q[7];
cx q[9],q[2];
h q[12];
cx q[9],q[6];
y q[7];
rz(0.6286555281683881) q[10];
cx q[4],q[5];
y q[5];
y q[13];
rz(1.2154038069920456) q[7];
rx(2.284661366303957) q[8];
rx(0.7273856311806477) q[2];
rx(6.103324226420383) q[8];
ry(2.720578195198957) q[13];
y q[11];
s q[10];
h q[7];
s q[11];
t q[11];
ry(4.766567335459742) q[9];
rx(5.517622113126137) q[11];
cz q[9],q[5];
rz(2.738697716654763) q[4];
z q[11];
x q[7];
ry(0.9646067882777152) q[2];
s q[9];
h q[0];
rz(2.793168155307437) q[3];
rx(1.9924041166324504) q[8];
x q[8];
s q[5];
cx q[5],q[4];
y q[8];
ry(0.5910087089385755) q[11];
z q[10];
y q[11];
t q[7];
cz q[0],q[7];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
rz(1.4826818544450509) q[0];
h q[0];
h q[1];
rz(2.793168155307437) q[3];
rx(5.909672773479288) q[4];
h q[4];
ry(pi) q[5];
rz(pi/2) q[6];
rz(1.9261888465977481) q[7];
rx(-3*pi/4) q[7];
cx q[0],q[7];
h q[7];
h q[8];
cx q[1],q[8];
ry(2.526408075382306) q[8];
rz(pi/2) q[8];
rz(4.679157984357947) q[9];
h q[9];
cx q[9],q[4];
h q[4];
cx q[4],q[5];
rz(2.738697716654763) q[4];
ry(pi) q[5];
h q[5];
ry(5.19021539939376) q[9];
cx q[9],q[2];
rx(0.7273856311806477) q[2];
ry(0.9646067882777152) q[2];
cx q[9],q[6];
ry(4.766567335459742) q[9];
cx q[9],q[5];
h q[5];
rz(pi/2) q[5];
cx q[5],q[4];
rz(2.385235907207941) q[9];
h q[10];
rz(6.251973477053568) q[10];
rz(-0.01607357669392062) q[11];
ry(0.9289231914110643) q[11];
rz(1.045397163134572) q[11];
ry(-1.1667851935371683) q[12];
ry(-0.4210144583908362) q[13];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
x q[2];
cx q[4],q[2];
cz q[13],q[4];
z q[11];
y q[13];
rz(4.302399126381679) q[10];
rz(4.1424760047965155) q[13];
y q[13];
x q[6];
cx q[12],q[5];
h q[8];
s q[3];
h q[3];
rx(3.608469115345701) q[4];
rz(0.4706815419919275) q[5];
cx q[2],q[9];
cz q[6],q[11];
cx q[0],q[2];
z q[10];
cz q[13],q[6];
h q[1];
y q[9];
cz q[10],q[4];
cz q[8],q[10];
cz q[2],q[1];
rz(0.3253659522240325) q[3];
t q[7];
rz(2.1448744966915387) q[2];
rz(3.653797058759521) q[3];
rx(4.5134000325238475) q[6];
cx q[2],q[9];
z q[8];
cx q[10],q[1];
z q[10];
z q[4];
cz q[5],q[13];
rz(5.008883620445975) q[2];
cz q[3],q[6];
ry(3.9148371446715857) q[0];
cz q[4],q[5];
cz q[5],q[12];
t q[4];
y q[8];
cx q[0],q[13];
t q[1];
cz q[2],q[6];
ry(1.8554306488512342) q[6];
x q[2];
y q[10];
t q[6];
cz q[5],q[2];
z q[3];
cz q[8],q[5];
cz q[4],q[2];
z q[13];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
x q[2];
rx(-pi/2) q[3];
rz(-0.7332259694011363) q[3];
cx q[4],q[2];
h q[4];
x q[6];
rz(pi/4) q[7];
h q[8];
cx q[2],q[9];
cx q[0],q[2];
x q[5];
x q[5];
ry(3.9148371446715857) q[0];
cx q[2],q[1];
h q[1];
rz(7.153758117137514) q[2];
ry(pi) q[9];
cx q[2],q[9];
rz(10.585584433561266) q[10];
x q[4];
x q[4];
ry(pi/2) q[11];
cx q[6],q[11];
h q[6];
h q[11];
cx q[12],q[5];
rz(0.4706815419919275) q[5];
h q[12];
cx q[13],q[4];
rz(-2.6747161918338858) q[4];
cx q[10],q[4];
h q[4];
rz(5*pi/4) q[4];
h q[10];
cx q[8],q[10];
rx(pi) q[8];
h q[10];
cx q[10],q[1];
rz(pi/4) q[1];
ry(pi) q[10];
rz(2.1407093023830708) q[13];
cx q[13],q[6];
x q[8];
x q[8];
rz(-1.7697852746557388) q[6];
cx q[3],q[6];
cx q[2],q[6];
ry(-pi/2) q[2];
ry(2.856958331533456) q[6];
rz(-3*pi/4) q[6];
h q[13];
cx q[5],q[13];
h q[5];
cx q[4],q[5];
h q[5];
cx q[5],q[12];
cx q[5],q[2];
cx q[4],q[2];
h q[2];
h q[5];
cx q[8],q[5];
h q[5];
h q[12];
h q[13];
cx q[0],q[13];
rz(pi) q[13];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
Are these two 14-qubit circuits equivalent (do they implement the same unitary up to global phase)?

Circuit A (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
z q[1];
cz q[2],q[1];
y q[10];
t q[7];
cz q[2],q[1];
rz(0.643490595348736) q[9];
x q[13];
cx q[13],q[2];
s q[13];
t q[10];
x q[5];
cz q[0],q[13];
s q[10];
ry(4.13429172494234) q[7];
ry(4.808795900868258) q[8];
cz q[4],q[11];
cx q[8],q[4];
cx q[0],q[11];
rx(0.8874690506960367) q[13];
y q[12];
cx q[3],q[4];
ry(5.243404530617571) q[11];
x q[5];
h q[1];
rx(4.1202803642574) q[3];
rx(1.7512732600390188) q[5];
x q[2];
x q[12];
cz q[1],q[5];
x q[5];
ry(2.9805225904958217) q[5];
y q[7];
cx q[13],q[2];
cx q[5],q[11];
rx(4.157377053192782) q[3];
y q[4];
y q[11];
cx q[12],q[0];
cx q[8],q[3];
s q[6];
x q[2];
ry(4.637618986216838) q[5];
s q[0];
ry(2.938812261503058) q[8];
y q[5];
cx q[6],q[11];
rx(2.2883048916281914) q[13];
s q[10];
x q[8];
cz q[0],q[6];
rz(2.3464623514216814) q[12];
z q[5];
cz q[7],q[0];
cx q[7],q[3];
cz q[5],q[9];
```

Circuit B (OpenQASM 2.0):
```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[14];
ry(pi/2) q[1];
rx(2.3158776257216154) q[5];
h q[5];
cx q[1],q[5];
ry(-1.731866389888868) q[5];
rz(pi/2) q[6];
rz(pi/4) q[7];
ry(0.9926990713525468) q[7];
ry(5.555633855441001) q[8];
rz(0.643490595348736) q[9];
h q[9];
ry(3.913395927590104) q[10];
rz(5*pi/4) q[10];
h q[11];
cx q[4],q[11];
cx q[8],q[4];
cx q[3],q[4];
rx(8.277657417450182) q[3];
ry(pi) q[4];
cx q[8],q[3];
ry(2.938812261503058) q[8];
x q[8];
h q[11];
rz(-0.7951303021681118) q[12];
x q[13];
cx q[13],q[2];
rz(pi/2) q[13];
h q[13];
cx q[0],q[13];
cx q[0],q[11];
ry(5.243404530617571) q[11];
cx q[5],q[11];
rz(-pi) q[5];
ry(-1.4960263326270447) q[5];
cx q[5],q[9];
h q[9];
ry(pi) q[11];
cx q[6],q[11];
h q[6];
cx q[12],q[0];
rz(pi/2) q[0];
cx q[0],q[6];
h q[0];
h q[6];
cx q[7],q[0];
h q[0];
cx q[7],q[3];
h q[13];
rx(0.8874690506960367) q[13];
cx q[13],q[2];
rx(2.2883048916281914) q[13];
```

Determine equivalence. You may use any approach: gate identity reasoning, ZX-calculus, simulation, or any other method.

Write a function `solve()` that returns True if the circuits are equivalent (same unitary up to global phase), or False if they are not.


Prompt:
The following quantum circuit operates on 3 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[3];
cx q[2],q[0];
rz(2.284789119577985) q[1];
cx q[0],q[2];
rz(6.231562207906491) q[0];
```

Map this circuit to a device with 5 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 3 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[3];
cx q[2],q[1];
cx q[2],q[0];
```

Map this circuit to a device with 5 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 3 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[3];
cx q[2],q[0];
cx q[2],q[1];
```

Map this circuit to a device with 5 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 3 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[3];
cx q[2],q[0];
cx q[1],q[0];
rz(2.282957393933801) q[1];
```

Map this circuit to a device with 5 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 3 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[3];
cx q[2],q[0];
cx q[0],q[2];
```

Map this circuit to a device with 5 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 5 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 5 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 4 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
cx q[0],q[2];
cx q[0],q[2];
cx q[2],q[1];
cx q[1],q[0];
cx q[3],q[1];
rz(4.5399399394392095) q[0];
```

Map this circuit to a device with 6 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 4 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
cx q[3],q[1];
cx q[3],q[0];
rz(4.36559303510342) q[1];
cx q[1],q[0];
cx q[0],q[3];
cx q[3],q[0];
```

Map this circuit to a device with 6 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 4 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
cx q[3],q[1];
cx q[1],q[3];
rz(3.795291598684939) q[2];
cx q[1],q[3];
cx q[3],q[0];
cx q[1],q[3];
rz(4.587769480680755) q[1];
```

Map this circuit to a device with 6 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 4 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
cx q[0],q[2];
rz(3.9226505986372455) q[2];
cx q[1],q[3];
rz(4.498088868271407) q[3];
cx q[2],q[0];
cx q[2],q[1];
rz(3.318174983115968) q[0];
cx q[0],q[1];
rz(5.1810652839065146) q[1];
```

Map this circuit to a device with 6 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 4 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[4];
cx q[0],q[1];
cx q[0],q[1];
cx q[1],q[2];
cx q[0],q[3];
cx q[1],q[2];
```

Map this circuit to a device with 6 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 6 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 6 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 5 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[5];
cx q[1],q[3];
cx q[3],q[2];
cx q[4],q[1];
rz(1.5349439970466117) q[0];
cx q[0],q[4];
cx q[4],q[1];
cx q[3],q[4];
cx q[3],q[2];
cx q[1],q[2];
```

Map this circuit to a device with 7 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 5 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[5];
cx q[3],q[1];
cx q[3],q[0];
cx q[4],q[2];
cx q[4],q[0];
cx q[2],q[0];
rz(5.351157746381014) q[4];
cx q[1],q[4];
cx q[0],q[2];
rz(2.3698183379520237) q[2];
cx q[2],q[3];
```

Map this circuit to a device with 7 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 5 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[5];
cx q[0],q[4];
rz(1.735827999833344) q[3];
cx q[3],q[4];
cx q[4],q[2];
cx q[0],q[3];
cx q[0],q[1];
rz(5.727811035769594) q[3];
cx q[2],q[1];
cx q[4],q[0];
cx q[4],q[3];
rz(0.23231044554829244) q[3];
```

Map this circuit to a device with 7 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 5 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[5];
cx q[0],q[4];
rz(5.522406171766144) q[4];
cx q[1],q[3];
cx q[1],q[3];
cx q[1],q[4];
cx q[2],q[4];
cx q[1],q[4];
rz(3.0560856552576325) q[2];
cx q[0],q[1];
rz(4.996651422508294) q[0];
cx q[4],q[2];
```

Map this circuit to a device with 7 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 5 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[5];
cx q[2],q[1];
cx q[1],q[3];
cx q[3],q[1];
cx q[0],q[3];
rz(0.6309146082747762) q[0];
cx q[3],q[0];
cx q[2],q[4];
cx q[4],q[1];
cx q[1],q[3];
```

Map this circuit to a device with 7 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 7 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 7 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 7 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
cx q[0],q[3];
cx q[6],q[0];
cx q[6],q[1];
cx q[0],q[2];
rz(2.414735894460961) q[3];
cx q[4],q[0];
cx q[0],q[2];
rz(0.41811569544635546) q[0];
cx q[3],q[5];
rz(3.1348290892704624) q[0];
cx q[1],q[4];
rz(2.3140264400830906) q[4];
cx q[3],q[6];
cx q[5],q[1];
cx q[2],q[4];
rz(0.42874143515397933) q[2];
cx q[5],q[3];
```

Map this circuit to a device with 9 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 7 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
cx q[5],q[4];
rz(5.919715403701441) q[0];
cx q[6],q[4];
rz(6.191429131053792) q[6];
cx q[1],q[6];
cx q[1],q[6];
rz(5.931891424771653) q[4];
cx q[5],q[1];
cx q[5],q[4];
cx q[6],q[5];
rz(3.231267583401835) q[5];
cx q[3],q[5];
rz(3.9609828642098486) q[2];
cx q[6],q[0];
rz(4.727754342911764) q[4];
cx q[3],q[2];
cx q[5],q[3];
rz(4.7463874224956655) q[2];
cx q[0],q[2];
rz(4.981694506209259) q[6];
```

Map this circuit to a device with 9 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 7 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
cx q[5],q[6];
rz(6.104872221436945) q[2];
cx q[5],q[6];
cx q[0],q[6];
rz(5.5834130220724845) q[6];
cx q[5],q[3];
rz(2.5310080093163614) q[4];
cx q[1],q[0];
cx q[1],q[5];
cx q[5],q[2];
cx q[2],q[0];
cx q[5],q[0];
cx q[1],q[0];
cx q[4],q[2];
cx q[1],q[6];
```

Map this circuit to a device with 9 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 7 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
cx q[3],q[1];
cx q[5],q[1];
rz(3.521966798448869) q[1];
cx q[1],q[2];
rz(2.3634462525311553) q[6];
cx q[6],q[3];
cx q[3],q[6];
cx q[1],q[2];
rz(0.4283196418696909) q[3];
cx q[5],q[1];
cx q[4],q[2];
cx q[6],q[4];
cx q[6],q[2];
cx q[4],q[5];
rz(5.278910766928672) q[1];
cx q[3],q[5];
```

Map this circuit to a device with 9 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 7 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[7];
cx q[4],q[2];
rz(2.6523190670871397) q[4];
cx q[3],q[2];
rz(3.562063793550325) q[4];
cx q[2],q[6];
rz(3.1764206838126356) q[6];
cx q[0],q[6];
cx q[0],q[5];
cx q[6],q[1];
cx q[1],q[0];
rz(4.525343995271579) q[4];
cx q[4],q[1];
cx q[6],q[5];
rz(0.265050513446331) q[5];
cx q[0],q[3];
cx q[0],q[5];
rz(1.796947653432336) q[0];
cx q[0],q[1];
```

Map this circuit to a device with 9 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 9 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 9 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 10 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
cx q[9],q[5];
rz(5.022177120804256) q[8];
cx q[8],q[9];
cx q[1],q[2];
cx q[6],q[8];
rz(5.673081358880238) q[6];
cx q[0],q[2];
cx q[7],q[3];
rz(1.726006211026131) q[3];
cx q[5],q[7];
rz(6.147431845307644) q[3];
cx q[0],q[5];
cx q[0],q[4];
rz(4.598095134420014) q[5];
cx q[6],q[5];
rz(4.059661402883541) q[0];
cx q[2],q[4];
cx q[8],q[4];
rz(1.7801064889693083) q[3];
cx q[1],q[8];
rz(2.9818211567871225) q[3];
cx q[5],q[1];
rz(3.077760183802101) q[2];
cx q[9],q[0];
rz(6.259996726195062) q[8];
cx q[3],q[5];
cx q[1],q[5];
cx q[4],q[3];
rz(4.213254482932426) q[8];
```

Map this circuit to a device with 12 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 10 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
cx q[8],q[9];
cx q[5],q[3];
cx q[8],q[9];
cx q[5],q[1];
cx q[5],q[4];
rz(3.0763749920771226) q[4];
cx q[3],q[2];
cx q[6],q[4];
cx q[8],q[1];
rz(4.24316164988852) q[5];
cx q[0],q[8];
cx q[7],q[1];
rz(2.225559308716508) q[1];
cx q[4],q[9];
rz(2.6036604343617165) q[1];
cx q[9],q[3];
rz(4.3145382906363015) q[6];
cx q[2],q[6];
rz(6.270055118642815) q[3];
cx q[4],q[1];
rz(0.026992685998655862) q[7];
cx q[9],q[0];
cx q[2],q[3];
cx q[4],q[2];
cx q[0],q[9];
```

Map this circuit to a device with 12 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 10 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
cx q[6],q[4];
rz(5.903631994897631) q[1];
cx q[9],q[4];
cx q[2],q[1];
cx q[4],q[9];
rz(5.747657259314519) q[7];
cx q[1],q[9];
cx q[1],q[8];
cx q[3],q[8];
cx q[0],q[4];
cx q[0],q[3];
cx q[6],q[1];
rz(1.4050438213885217) q[7];
cx q[9],q[0];
cx q[1],q[0];
cx q[6],q[1];
cx q[5],q[1];
rz(2.057753015580604) q[7];
cx q[4],q[6];
cx q[6],q[9];
rz(2.840368896821549) q[7];
cx q[3],q[0];
rz(5.17253891302812) q[4];
cx q[4],q[5];
```

Map this circuit to a device with 12 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 10 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
cx q[9],q[1];
rz(0.21851371773850076) q[9];
cx q[3],q[0];
rz(2.399006727514206) q[9];
cx q[4],q[8];
cx q[8],q[6];
rz(6.116504181526717) q[1];
cx q[6],q[9];
rz(4.270364081620882) q[6];
cx q[1],q[6];
rz(4.107854540356539) q[9];
cx q[8],q[1];
cx q[3],q[9];
rz(2.7976416542078946) q[8];
cx q[2],q[0];
cx q[8],q[9];
cx q[6],q[0];
rz(1.7224735541657494) q[4];
cx q[0],q[7];
rz(4.006509161932251) q[6];
cx q[1],q[7];
cx q[3],q[7];
rz(0.3766765352450249) q[7];
cx q[6],q[3];
rz(1.8455765641641404) q[6];
cx q[5],q[9];
cx q[2],q[8];
rz(3.7720322034224862) q[1];
cx q[2],q[9];
rz(3.290740753412172) q[7];
```

Map this circuit to a device with 12 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
The following quantum circuit operates on 10 logical qubits:

```
OPENQASM 2.0;
include "qelib1.inc";
qreg q[10];
cx q[4],q[6];
rz(1.0849420259468958) q[7];
cx q[1],q[8];
cx q[4],q[8];
cx q[8],q[6];
cx q[9],q[8];
rz(3.6008272129148207) q[1];
cx q[1],q[4];
cx q[0],q[3];
rz(6.123269437251737) q[7];
cx q[0],q[1];
rz(3.431140520847325) q[2];
cx q[5],q[9];
cx q[3],q[8];
cx q[9],q[5];
rz(1.062109449312094) q[9];
cx q[4],q[0];
cx q[8],q[2];
cx q[6],q[4];
cx q[0],q[3];
cx q[1],q[0];
cx q[6],q[5];
rz(0.32124003290525405) q[8];
cx q[7],q[2];
```

Map this circuit to a device with 12 physical qubits and connectivity:
[(0,1), (1,2), (2,3), (3,4), (4,5), (5,6), (6,7), (7,8), (8,9), (9,10), (10,11)]

Requirements:
- Insert SWAP gates so ALL two-qubit gates act on connected qubit pairs.
- The mapped circuit must be functionally equivalent to the original.
- Minimize the number of inserted SWAPs.
- Do NOT use qiskit.transpile() or any PassManager. Build the routed circuit manually using QuantumCircuit methods (cx, swap, etc.).
- The output circuit must use 12 qubits. Map logical qubit i to physical qubit i (identity initial layout).

Write a Qiskit function `solve()` that returns the routed QuantumCircuit on 12 qubits. Use only cx and swap gates for 2-qubit operations.


Prompt:
Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |00>.

Circuit (4 gates applied in order):
  t on qubits [0]
  s on qubits [0]
  cx on qubits [0, 1]
  y on qubits [1]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.01
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.05
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |00>.

Circuit (4 gates applied in order):
  ry(0.150202) on qubits [1]
  x on qubits [0]
  s on qubits [1]
  t on qubits [1]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.01
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.05
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |00>.

Circuit (4 gates applied in order):
  y on qubits [1]
  cx on qubits [0, 1]
  h on qubits [0]
  ry(1.200757) on qubits [0]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.01
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.05
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |00>.

Circuit (4 gates applied in order):
  h on qubits [0]
  y on qubits [0]
  x on qubits [0]
  rz(4.223213) on qubits [1]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.01
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.05
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 2-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |00>.

Circuit (4 gates applied in order):
  cx on qubits [1, 0]
  h on qubits [1]
  s on qubits [1]
  ry(1.337598) on qubits [0]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.01
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.05
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |000>.

Circuit (8 gates applied in order):
  cx on qubits [0, 2]
  t on qubits [2]
  y on qubits [0]
  s on qubits [0]
  cx on qubits [0, 2]
  h on qubits [1]
  rz(1.045059) on qubits [2]
  ry(3.592956) on qubits [0]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.005
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.02
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |000>.

Circuit (8 gates applied in order):
  rx(0.642837) on qubits [2]
  cx on qubits [1, 0]
  s on qubits [0]
  cx on qubits [1, 2]
  cx on qubits [2, 1]
  cx on qubits [2, 1]
  h on qubits [1]
  s on qubits [2]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.005
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.02
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |000>.

Circuit (8 gates applied in order):
  y on qubits [2]
  ry(3.834888) on qubits [1]
  x on qubits [0]
  y on qubits [2]
  cx on qubits [2, 0]
  s on qubits [0]
  h on qubits [2]
  h on qubits [1]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.005
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.02
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |000>.

Circuit (8 gates applied in order):
  x on qubits [0]
  s on qubits [2]
  cx on qubits [2, 1]
  z on qubits [1]
  cx on qubits [2, 0]
  t on qubits [0]
  t on qubits [2]
  cx on qubits [0, 1]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.005
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.02
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 3-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |000>.

Circuit (8 gates applied in order):
  ry(4.374501) on qubits [2]
  s on qubits [0]
  y on qubits [2]
  ry(3.504125) on qubits [1]
  s on qubits [1]
  t on qubits [0]
  x on qubits [1]
  y on qubits [1]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.005
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.02
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |0000>.

Circuit (15 gates applied in order):
  s on qubits [2]
  x on qubits [1]
  cx on qubits [0, 2]
  cx on qubits [3, 0]
  rz(6.136252) on qubits [1]
  z on qubits [0]
  t on qubits [0]
  ry(1.381243) on qubits [1]
  h on qubits [3]
  x on qubits [1]
  s on qubits [1]
  y on qubits [1]
  h on qubits [1]
  x on qubits [1]
  y on qubits [0]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.003
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.015
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |0000>.

Circuit (15 gates applied in order):
  z on qubits [1]
  s on qubits [3]
  cx on qubits [1, 0]
  x on qubits [0]
  cx on qubits [2, 3]
  rx(5.926695) on qubits [3]
  cx on qubits [2, 1]
  y on qubits [3]
  cx on qubits [1, 0]
  z on qubits [2]
  cx on qubits [1, 3]
  z on qubits [2]
  s on qubits [3]
  rz(2.584050) on qubits [2]
  cx on qubits [2, 3]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.003
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.015
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.


Prompt:
Given this 4-qubit quantum circuit and noise model, predict the output state fidelity F = <psi_ideal|rho_noisy|psi_ideal>.

The initial state is |0000>.

Circuit (15 gates applied in order):
  s on qubits [0]
  cx on qubits [2, 3]
  z on qubits [0]
  cx on qubits [1, 2]
  t on qubits [0]
  y on qubits [2]
  rx(3.743972) on qubits [3]
  s on qubits [1]
  cx on qubits [3, 1]
  x on qubits [2]
  rx(3.686055) on qubits [2]
  x on qubits [0]
  t on qubits [3]
  s on qubits [0]
  z on qubits [1]

Noise model: depolarizing noise applied AFTER each gate.
  - After each 1-qubit gate: depolarizing channel with probability p = 0.003
    D_1(rho) = (1-p)*rho + (p/3)*(X*rho*X + Y*rho*Y + Z*rho*Z)
  - After each 2-qubit gate: depolarizing channel with probability p = 0.015
    D_2(rho) = (1-p)*rho + (p/15)*sum_{P in Paulis\II} P*rho*P
    (sum over all 15 non-identity two-qubit Pauli operators)

Standard gate definitions:
  h: (1/sqrt(2))*[[1,1],[1,-1]]
  x: [[0,1],[1,0]]
  y: [[0,-i],[i,0]]
  z: [[1,0],[0,-1]]
  s: [[1,0],[0,i]]
  t: [[1,0],[0,exp(i*pi/4)]]
  rx(theta): [[cos(t/2), -i*sin(t/2)], [-i*sin(t/2), cos(t/2)]]
  ry(theta): [[cos(t/2), -sin(t/2)], [sin(t/2), cos(t/2)]]
  rz(theta): [[exp(-i*t/2), 0], [0, exp(i*t/2)]]
  cx: CNOT (control, target) in computational basis

Multi-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} ⊗ ... ⊗ Gate_k ⊗ ... ⊗ I_0.

Write a function `solve()` that returns a float (the predicted fidelity).
You may use numpy. Do NOT use qiskit, qiskit_aer, or any quantum simulation library.
Implement density matrix propagation from scratch.