Optimal Control by Variational Quantum Algorithms

Hybrid quantum-classical algorithms hold great promise for solving quantum control problems on near-term quantum computers. In this work, we employ the hybrid framework that integrates digital quantum simulation with classical optimization to achieve optimal engineering of quantum many-body systems. To evaluate the overall performance of this method, we introduce a general metric termed control optimality, which accounts for constraints on both classical and quantum components. As a concrete example, we investigate the time-optimal control for perfect state transfer in a one-dimensional spin model using the variational quantum algorithm, closely approaching the quantum speed limit. Moreover, we discuss the emergent gradient behavior and error robustness, demonstrating the feasibility of applying hybrid quantum algorithms to solve quantum optimal control problems. These results establish a systematic framework for hybrid algorithms to address quantum control problems on near-term quantum platforms.