When Does Adaptation Win? Scaling Laws for Meta-Learning in Quantum Control
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| Format: | Preprint |
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2026
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| _version_ | 1866910238100160512 |
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| author | Leclerc, Nima Miller, Chris Brawand, Nicholas |
| author_facet | Leclerc, Nima Miller, Chris Brawand, Nicholas |
| contents | Quantum hardware suffers from intrinsic device heterogeneity and environmental drift, forcing practitioners to choose between suboptimal non-adaptive controllers or costly per-device recalibration. We derive a scaling law lower bound for meta-learning showing that the adaptation gain (expected fidelity improvement from task-specific gradient steps) saturates exponentially with gradient steps and scales linearly with task variance, providing a quantitative criterion for when adaptation justifies its overhead. Validation on quantum gate calibration shows negligible benefits for low-variance tasks but >40% fidelity gains on two-qubit gates under extreme out-of-distribution conditions (10$\times$ the training noise), with implications for reducing per-device calibration time on cloud quantum processors. Further validation on classical linear-quadratic control confirms these laws emerge from general optimization geometry rather than quantum-specific physics. We further introduce a few-shot pre-adaptation protocol that estimates the optimal adaptation budget from $N{=}3$-5 probe steps within 3-19% relative error across out-of-distribution regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18973 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | When Does Adaptation Win? Scaling Laws for Meta-Learning in Quantum Control Leclerc, Nima Miller, Chris Brawand, Nicholas Machine Learning Artificial Intelligence Systems and Control Quantum Physics Quantum hardware suffers from intrinsic device heterogeneity and environmental drift, forcing practitioners to choose between suboptimal non-adaptive controllers or costly per-device recalibration. We derive a scaling law lower bound for meta-learning showing that the adaptation gain (expected fidelity improvement from task-specific gradient steps) saturates exponentially with gradient steps and scales linearly with task variance, providing a quantitative criterion for when adaptation justifies its overhead. Validation on quantum gate calibration shows negligible benefits for low-variance tasks but >40% fidelity gains on two-qubit gates under extreme out-of-distribution conditions (10$\times$ the training noise), with implications for reducing per-device calibration time on cloud quantum processors. Further validation on classical linear-quadratic control confirms these laws emerge from general optimization geometry rather than quantum-specific physics. We further introduce a few-shot pre-adaptation protocol that estimates the optimal adaptation budget from $N{=}3$-5 probe steps within 3-19% relative error across out-of-distribution regimes. |
| title | When Does Adaptation Win? Scaling Laws for Meta-Learning in Quantum Control |
| topic | Machine Learning Artificial Intelligence Systems and Control Quantum Physics |
| url | https://arxiv.org/abs/2601.18973 |