2025/02/27 by Penghui Wang, Shan Wang, Penghui, Wang +3
Computer Science · Physics and Astronomy · Economics, Econometrics and Finance · #Quantum Information and Cryptography #Laser-Matter Interactions and Applications #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2502.19666
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 Lü and Zhang's approach [Q. Lü 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.