IEEE/CAA Journal of Automatica Sinica
Citation:  S. Cong and Z. Dong, “Pure state feedback switching control based on the online estimated state for stochastic open quantum systems,” IEEE/CAA J. Autom. Sinica, vol. 11, no. 10, pp. 2166–2178, Oct. 2024. doi: 10.1109/JAS.2023.124071 
For the nqubit stochastic open quantum systems, based on the Lyapunov stability theorem and LaSalle’s invariant set principle, a pure state switching control based on online estimated state feedback (short for OQSTSFC) is proposed to realize the state transition the pure state of the target state including eigenstate and superposition state. The proposed switching control consists of a constant control and a control law designed based on the Lyapunov method, in which the Lyapunov function is the state distance of the system. The constant control is used to drive the system state from an initial state to the convergence domain only containing the target state, and a Lyapunovbased control is used to make the state enter the convergence domain and then continue to converge to the target state. At the same time, the continuous weak measurement of quantum system and the quantum state tomography method based on the online alternating direction multiplier (QSTOADM) are used to obtain the system information and estimate the quantum state which is used as the input of the quantum system controller. Then, the pure state feedback switching control method based on the online estimated state feedback is realized in an nqubit stochastic open quantum system. The complete derivation process of nqubit QSTOADM algorithm is given; Through strict theoretical proof and analysis, the convergence conditions to ensure any initial state of the quantum system to converge the target pure state are given. The proposed control method is applied to a 2qubit stochastic open quantum system for numerical simulation experiments. Four possible different position cases between the initial estimated state and that of the controlled system are studied and discussed, and the performances of the state transition under the corresponding cases are analyzed.
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