Real-Time Quantum Feedback Control: ManipulatingQuantum State in Non-Markovian System

In this paper, we propose a closed-loop real-time feedback design for manipulating a quantum state to a target eigenstate via sequential measurements. To this end, based on the Lyapunov stability theorem, considering the controllability and convergence of the system, we select one measured observable and two control channels, which feedback part of the output signal to the input end, forming a closed-loop control. By dynamical programming, we find the optimal parameters to achieve state transfer with a high probability by real-time feedback control. Numerical simulation experiments show that, in a stochastic quantum system with non-Markovian noise, the real-time control strategy moves the system from initial state to the target eigenstate with fast convergence.