Feedback Control Of Stochastic Open Quantum Systems

In practical applications,quantum systems are often affected by the external environment and measurement factors and become stochastic open quantum systems.Therefore,the research on the control of stochastic open quantum systems has important application value and development prospects.Using the online quantum state estimation algorithm,the estimated states of the quantum system can be obtained in real time.According to the estimated system states,combined with the corresponding control strategy,the feedback control of the system can be realized.This dissertation focuses on the state transfer and feedback control based on online state estimation of stochastic open quantum systems.The research contents include the following three aspects:1.Based on the Lyapunov stability theorem and LaSalle’s invariance theorem,a switching control strategy is proposed to realize the state transfer of stochastic open quantum systems for the case that the target states are pure states.The proposed switching control consists of a constant control and a control law designed based on Lyapunov method.The Lyapunov function is the state distance of the system.The constant control is used to drive the system state from the initial state to the convergence domain containing the target state,and Lyapunov control is used to make the state in the convergence region continue to converge to the desired target state.The proposed control method is applied to a 2-qubit stochastic open quantum system,and the performance is compared with the existing switching control law of eigenstates.The experimental results show the superiority of the proposed control law.2.For n-qubit stochastic open quantum systems,an estimated-based-state switching feedback control is proposed to realize the pure state transfer of stochastic open quantum systems.The system information is obtained by the continuous weak measurement and the online alternating direction multiplier method for online quantum estimation(QST-OADM),and the states for feedback control are online estimated.Then,the state transfer is relized based on the estimated states and the pure state switching feedback control method for stochastic open quantum system.The convergence of QST-OADM algorithm is proved,and the selection range of estimation parameters and control parameters are given.In numerical simulation experiments,the performance of the online estimation algorithm without control is verified,and the effects of different initial real states and initial estimated states on the performance of the state transfer are investigated.3.Based on quantum state online estimation and Lyapunov stability theorem,the state feedback control of n-qubit stochastic open quantum system is proposed to realize the state transfer from any initial state to any target state.Combining the quantum continuous weak measurement and the quantum state estimation method QST-OADM,the real-time estimated states are obtained for the state feedback of the controlled system.The state feedback control law is designed by combining multiple controls,one of which is used to overcome the system drift term and the others are used to realize the state transfer.At the same time,the mathematical proof of the stability of the closed-loop control system is given based on the Lyapunov stability theorem.Numerical simulation experiments verify the effectiveness of the proposed control method in the transfer between different initial states and different target states.