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arXiv:2604.19990 · Physical Review A

Reinforcement Learning for Robust Calibration of Multi-Qudit Quantum Gates

Amine Jaouadi, Sahel Ashhab

quant-phSubmitted Apr 21, 2026• Announced Apr 23, 2026• 1 citation• Revised Aug 26, 2026 (v2)
v1 · Apr 21, 2026v2 · Aug 26, 2026v3 · Aug 29, 2026
arXivHTMLPDF

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.

Journal reference
Phys. Rev. A 114, 022463 (2026)
DOI
10.1103/717q-ypkg
Comments
13 pages, 13 figues

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Quantum control requires high-precision and robust control pulses to ensure optimal system performance. However, control sequences generated with a system model may suffer from model bias, leading to low fidelity. While model-free reinforcement learning (RL) methods have been developed to avoid such biases, training an RL agent from scratch can be time-consuming, often taking hours to gather enough samples for convergence. This challenge has hindered the broad application of RL techniques to larger and more complex quantum control issues, limiting their adaptability. In this work, we use Reinforcement Learning from Demonstration (RLfD) to leverage the control sequences generated with system models and further optimize them with RL to avoid model bias. By avoiding learning from scratch and starting with reasonable control pulse shapes, this approach can increase sample efficiency by reducing the number of samples, which can significantly reduce the training time. Thus, this method can effectively handle pulse shapes that are discretized into more than 1000 pieces without compromising final fidelity. We have simulated the preparation of several high-fidelity non-classical states using the RLfD method. We also find that the training process is more stable when using RLfD. In addition, this method is suitable for fast gate calibration using reinforcement learning.
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The extreme sensitivity of contemporary hardware to noise, manufacturing variability, and imperfect quantum logic gates are key factors that limit hardware to reliably perform quantum computation at scale. The use of reinforcement learning assisted control techniques for system dynamics optimization in quantum gate control can significantly improve hardware performance and downstream computing power. However, con-trol field noise and Hamiltonian parameter uncertainty can lead to significant deviations from the target quantum gate. As a result, quantum gates lack the generalization ability to the quantum environment, and existing reinforcement learning assisted for quantum state preparation is not suitable for quantum gate control. In this paper, we design QcontrolSR, a state representation for reinforcement learning method, enabling quantum gate control with enhanced generalization ability. It requires no knowledge of a specific Hamiltonian model of the system, or its underlying unknown process. We introduce the state representation of quantum observations and show through demonstrations that QcontrolSR-optimized quantum gate control is insensitive to driving noise of the typical strength in practice. We show thatRx(π/2)R_{x}(\pi/2)Rx​(π/2)gate implemented using QcontrolSR can maintain fidelity greater than 0.95 and 0.99 on dynamical quantum stochastic system. The regions with fidelity greater than 0.99 and 0.999 are 2 and 3 times higher than the model-optimized Quantum gate control, respectively.