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

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. Together, these results offer a transferable framework for decision-making in adaptive control.

💡 Research Summary

The paper tackles a pressing practical problem in quantum computing: hardware devices exhibit significant heterogeneity and time‑varying noise, which forces frequent per‑device calibration. Traditional non‑adaptive controllers such as GRAPE are optimized for an average noise model and therefore become sub‑optimal for individual devices, while per‑device recalibration is costly in time and resources. The authors propose to use gradient‑based meta‑learning (MAML‑style) to learn a shared initialization of control parameters that can be rapidly adapted to each device with a few gradient steps.

The central theoretical contribution is the derivation of a scaling law for the “adaptation gap”
(G_K = \mathbb{E}_\xi