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

2026-01-26

AI Summary

This work addresses the limitations of non-adaptive quantum control strategies, which suffer from degraded performance or high calibration costs due to hardware heterogeneity and environmental drift. For the first time, the authors establish a quantitative scaling law that relates adaptive control gains to task variance and the number of gradient steps, revealing its efficacy under extreme out-of-distribution conditions. They demonstrate that this scaling law originates from a universal optimization geometry. Through meta-learning, scaling analysis, and quantum gate calibration experiments, the theory is validated: while adaptive gains yield negligible improvements in low-variance tasks, they enhance fidelity by over 40% in extreme out-of-distribution scenarios for two-qubit gates, substantially reducing calibration overhead on cloud-based quantum processors.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Adversarial Learning
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Security and Privacy: Large-scale security measurements
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• quantum control
• device heterogeneity
• environmental drift
• adaptive control
• meta-learning

Innovation

• scaling laws
• meta-learning
• quantum control
• adaptive control
• task variance