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<p>In this paper, we investigate the closed-loop solvability of the quantum stochastic linear quadratic optimal control problem. We derive the Pontryagin maximum principle for the linear quadratic control problem of infinite-dimensional quantum stochastic systems. We establish the relationships between the uniquely closed-loop solvability of quantum stochastic linear quadratic optimal control problems and the well-posedness of their corresponding Riccati equations. Inspired by Lü, Wang and Zhang’s ideas for stochastic Riccati equations (see Lü and Zhang (2021) and Lü and Wang (2023)), we prove the existence and uniqueness of the solutions to the quantum Riccati equations if the optimal strategy exists. The results provide a theoretical foundation for the optimal design of quantum control.</p>

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Quantum stochastic linear quadratic control theory: Closed-loop solvability

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Penghui Wang,
  • Shan Wang,
  • Shengkai Zhao

摘要

In this paper, we investigate the closed-loop solvability of the quantum stochastic linear quadratic optimal control problem. We derive the Pontryagin maximum principle for the linear quadratic control problem of infinite-dimensional quantum stochastic systems. We establish the relationships between the uniquely closed-loop solvability of quantum stochastic linear quadratic optimal control problems and the well-posedness of their corresponding Riccati equations. Inspired by Lü, Wang and Zhang’s ideas for stochastic Riccati equations (see Lü and Zhang (2021) and Lü and Wang (2023)), we prove the existence and uniqueness of the solutions to the quantum Riccati equations if the optimal strategy exists. The results provide a theoretical foundation for the optimal design of quantum control.