中国物理B ›› 2023, Vol. 32 ›› Issue (7): 70203-070203.doi: 10.1088/1674-1056/acb9f3

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Rapid stabilization of stochastic quantum systems in a unified framework

Jie Wen(温杰)1,†,‡, Fangmin Wang(王芳敏)2,†, Yuanhao Shi(史元浩)1, Jianfang Jia(贾建芳)1, and Jianchao Zeng(曾建潮)3,§   

  1. 1 School of Electrical and Control Engineering, North University of China, Taiyuan 030051, China;
    2 State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China;
    3 School of Computer Science and Technology, North University of China, Taiyuan 030051, China
  • 收稿日期:2022-11-09 修回日期:2023-02-05 接受日期:2023-02-08 出版日期:2023-06-15 发布日期:2023-06-29
  • 通讯作者: Jie Wen, Jianchao Zeng E-mail:wenjie015@gmail.com;zengjianchao@263.net
  • 基金资助:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 72071183), and Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2020-114).

Rapid stabilization of stochastic quantum systems in a unified framework

Jie Wen(温杰)1,†,‡, Fangmin Wang(王芳敏)2,†, Yuanhao Shi(史元浩)1, Jianfang Jia(贾建芳)1, and Jianchao Zeng(曾建潮)3,§   

  1. 1 School of Electrical and Control Engineering, North University of China, Taiyuan 030051, China;
    2 State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China;
    3 School of Computer Science and Technology, North University of China, Taiyuan 030051, China
  • Received:2022-11-09 Revised:2023-02-05 Accepted:2023-02-08 Online:2023-06-15 Published:2023-06-29
  • Contact: Jie Wen, Jianchao Zeng E-mail:wenjie015@gmail.com;zengjianchao@263.net
  • Supported by:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 72071183), and Research Project Supported by Shanxi Scholarship Council of China (Grant No. 2020-114).

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摘要： Rapid stabilization of general stochastic quantum systems is investigated based on the rapid stability of stochastic differential equations. We introduce a Lyapunov-LaSalle-like theorem for a class of nonlinear stochastic systems first, based on which a unified framework of rapidly stabilizing stochastic quantum systems is proposed. According to the proposed unified framework, we design the switching state feedback controls to achieve the rapid stabilization of single-qubit systems, two-qubit systems, and N-qubit systems. From the unified framework, the state space is divided into two state subspaces, and the target state is located in one state subspace, while the other system equilibria are located in the other state subspace. Under the designed state feedback controls, the system state can only transit through the boundary between the two state subspaces no more than two times, and the target state is globally asymptotically stable in probability. In particular, the system state can converge exponentially in (all or part of) the state subspace where the target state is located. Moreover, the effectiveness and rapidity of the designed state feedback controls are shown in numerical simulations by stabilizing GHZ states for a three-qubit system.

关键词: rapid stabilization, state feedback, stochastic quantum systems, switching control

Abstract: Rapid stabilization of general stochastic quantum systems is investigated based on the rapid stability of stochastic differential equations. We introduce a Lyapunov-LaSalle-like theorem for a class of nonlinear stochastic systems first, based on which a unified framework of rapidly stabilizing stochastic quantum systems is proposed. According to the proposed unified framework, we design the switching state feedback controls to achieve the rapid stabilization of single-qubit systems, two-qubit systems, and N-qubit systems. From the unified framework, the state space is divided into two state subspaces, and the target state is located in one state subspace, while the other system equilibria are located in the other state subspace. Under the designed state feedback controls, the system state can only transit through the boundary between the two state subspaces no more than two times, and the target state is globally asymptotically stable in probability. In particular, the system state can converge exponentially in (all or part of) the state subspace where the target state is located. Moreover, the effectiveness and rapidity of the designed state feedback controls are shown in numerical simulations by stabilizing GHZ states for a three-qubit system.

Key words: rapid stabilization, state feedback, stochastic quantum systems, switching control

中图分类号:  (Control theory)

  • 02.30.Yy
42.50.Lc (Quantum fluctuations, quantum noise, and quantum jumps)