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arXiv · 2502.19666

Quantum stochastic linear quadratic control theory: Closed-loop solvability

Wang Penghui·Wang Shan·Zhao Shengkai
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Abstract

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. The equivalence between unique closed-loop solvability for quantum stochastic linear quadratic optimal control problems and the well-posedness of the corresponding quantum Riccati equations is established. Notably, although the quantum Riccati equation is an infinite-dimensional deterministic operator-valued ordinary differential equation, classical methods are not applicable. Inspired by L\"{u} and Zhang's approach [Q. L\"{u} and X. Zhang, Probability Theory and Stochastic Modelling, 101. Springer, Cham, (2021) \& Mem. Amer. Math. Soc. 294 (2024)] to stochastic Riccati equations, we prove the existence and uniqueness of its solutions. The results provide a theoretical foundation for the optimal design of quantum control.

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Wang Penghui, Wang Shan, Zhao Shengkai. 2025-02-27. Quantum stochastic linear quadratic control theory: Closed-loop solvability. https://arxiv.org/abs/2502.19666

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