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

arXiv: https://arxiv.org/abs/2601.18973 · HTML: https://mlsanity.com/paper/2601.18973/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 47 references that are in the map.
- First posted on arXiv 26 Jan 2026.

## Builds on (most cited first, 10 of 10)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [On First-Order Meta-Learning Algorithms](https://mlsanity.com/paper/1803.02999/) (2018)
- [Linear Convergence of Gradient and Proximal-Gradient Methods Under the Polyak-Lojasiewicz Condition](https://mlsanity.com/paper/1608.04636/) (2016)
- [On the Convergence Theory of Gradient-Based Model-Agnostic Meta-Learning Algorithms](https://mlsanity.com/paper/1908.10400/) (2019)
- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [Quantum Circuit Optimization with AlphaTensor](https://mlsanity.com/paper/2402.14396/) (2024)
- [The effects of negative adaptation in Model-Agnostic Meta-Learning](https://mlsanity.com/paper/1812.02159/) (2018)
- [How to Build a Quantum Supercomputer: Scaling from Hundreds to Millions of Qubits](https://mlsanity.com/paper/2411.10406/) (2024)
- [How Does the Task Landscape Affect MAML Performance?](https://mlsanity.com/paper/2010.14672/) (2020)
- [A Lie Theoretic Framework for Controlling Open Quantum Systems](https://mlsanity.com/paper/2510.04719/) (2025)

## Built on by (most cited first, 1 of 1)

- [Adaptive Reinforcement Learning for Robust Open Quantum System Control: A Multi-Task Framework with Temporal Optimization](https://mlsanity.com/paper/2605.26925/) (2026)

## Abstract (arXiv)

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× 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.