Efficient closed-loop quantum control via Ansatz-ResPID protocol

Precise control of quantum devices is crucial for achieving high-fidelity operations in quantum computation and simulation. Among various noise sources in noisy intermediate-scale quantum (NISQ) devices, systematic drifts and fluctuations in the control Hamiltonian are particularly detrimental, as their effects accumulate over time and drive the system away from the desired dynamics. In this work, we introduce Ansatz-ResPID, a quantum adaptation of the classical closed-loop Proportional–Integral–Derivative (PID) controller, to stabilize quantum systems against Hamiltonian drift and fluctuation. Our method enables simultaneous stabilization of multiple control parameters while maintaining a simple, scalable, and easily parallelizable feedback structure. Its hyperparameters are automatically optimized through one-time learning, allowing robust application across a wide range of control settings and noise levels without prior knowledge or manual tuning. Compared to previous quantum feedback control and state-of-the-art reinforcement learning approaches, our method achieves comparable precision stabilization with an order of magnitude fewer feedback rounds. This work demonstrates a practical and efficient route toward scalable, high-fidelity control of quantum systems.