提出元学习适应收益的缩放定律，判断何时调整值得投入。
When Does Adaptation Win? Scaling Laws for Meta-Learning in Quantum Control
- 推导出适应增益随梯度步数指数饱和、与任务方差线性相关
- 极端分布外条件下两量子比特门提升超40%保真度
- 仅需3-5次探测即可预估最优调整次数，误差<19%
量子硬件受固有器件异质性和环境漂移影响，使用者常在次优的非自适应控制器与昂贵的逐设备校准间权衡。本文推导出元学习的缩放定律下界，表明适应增益（任务特定梯度步带来的期望保真度提升）随梯度步数指数饱和，且与任务方差线性相关，为适应是否值得付出开销提供了量化标准。在量子门校准上的验证显示，低方差任务收益微乎其微，但在极端分布外条件（训练噪声的10倍）下，两量子比特门保真度提升超过40%，对降低云量子处理器的逐设备校准时间具重要意义。在经典线性二次控制上的进一步验证表明，这些规律源于通用优化几何结构，而非量子特有物理。此外，我们提出一种少样本预适应协议，仅用3-5次探测步骤即可在分布外场景中以3-19%相对误差估计最优适应预算。
原文摘要 · Abstract (English)
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.
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