Reinforcement Learning for Robust Calibration of Multi-Qudit Quantum Gates

TL;DR

This paper introduces a hybrid optimization approach combining optimal control and deep reinforcement learning to calibrate high-fidelity, robust quantum gates for multi-qudit systems, addressing hardware variability.

Contribution

It presents a novel framework that uses reinforcement learning to refine control pulses, improving robustness against device parameter uncertainties in high-dimensional quantum systems.

Findings

Reinforcement learning learns residual corrections that improve gate robustness.

The method maintains high fidelity despite static model mismatches.

The approach is scalable and practical for real quantum hardware.

Abstract

Higher-dimensional quantum systems, such as qudits, offer architectural and algorithmic advantages over qubits, but their increased spectral crowding and limited controllability render high-fidelity quantum gates particularly challenging. We propose a hybrid optimization framework that integrates optimal control theory methods with contextual deep reinforcement learning to achieve robust controlled-phase gates on two qutrits. Optimal control is first used to design high-fidelity control pulses for a nominal system model. Reinforcement learning is then employed as a calibration stage that learns small residual corrections to these pulses in the presence of static model mismatch, thereby preserving good gate performance under realistic parameter uncertainties. By learning structured, low-dimensional residual corrections conditioned on device-specific parameter variations, reinforcement learning enhances the transfer robustness of nominally optimal but parameter-sensitive control solutions across ensembles of devices. Crucially, the reinforcement learning step in our framework does not compete with the optimal control step but provides the adaptability required for realistic hardware, systematically reducing the sensitivity to parameter fluctuations. Our results establish reinforcement learning as a practical and scalable ingredient for robust calibration of quantum gates in high-dimensional systems.