# Reproduction: When Does Adaptation Win? Scaling Laws for Meta-Learning in Quantum Control

[HF paper page](https://huggingface.co/papers/2601.18973)

## Pages

| Page |
| --- |
| [Executive summary](#/executive-summary) |
| [Claim 1: Scaling law for adaptation gain (Theorem 4.8)](#/claim-1-scaling-law-for-adaptation-gain-theorem-4-8) |
| [Claim 2: Single-qubit X-gate exponential saturation (R^2>0.99, beta~0.083)](#/claim-2-single-qubit-x-gate-exponential-saturation-r-2-0-99-beta-0-083) |
| [Claim 3: Two-qubit CZ under 10x noise: >40pp fidelity gain](#/claim-3-two-qubit-cz-under-10x-noise-40pp-fidelity-gain) |
| [Claim 4: Assumption 4.3 Polyak-Lojasiewicz curvature mu~0.03](#/claim-4-assumption-4-3-polyak-lojasiewicz-curvature-mu-0-03) |
| [Claim 5: Corollary 4.10: negligible benefit at low task variance](#/claim-5-corollary-4-10-negligible-benefit-at-low-task-variance) |
| [Claim 6: Classical LQR reproduces the exponential scaling law](#/claim-6-classical-lqr-reproduces-the-exponential-scaling-law) |
| [Conclusion](#/conclusion) |