Real-Time Optimal State Estimation-Based Feedback Control for Stochastic Quantum Systems in the Non-Markovian Case

This paper studies the real-time optimal state estimation-based feedback control for two-level stochastic quantum systems in the non-Markovian case. The system model is established by combining the time-convolutionless non-Markovian master equation and the stochastic master equation. A nonlinear filter based on the state-dependent Riccati equation is designed in order to achieve the real-time optimal estimation of quantum states. A quadratic function multiplied with an exponential term is selected as the Lyapunov function, and a continuous-time control law is deduced via the stochastic Lyapunov stability theorem to realize eigenstate feedback control based on real-time optimal state estimation. Numerical simulation results illustrate that the proposed control scheme is capable of steering the two-level quantum system from an arbitrary initial state to the desired eigenstate with a fidelity higher than 99% within a time of 3 a.u.