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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 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 |
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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.
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Received: 09 November 2022
Revised: 05 February 2023
Accepted manuscript online: 08 February 2023
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PACS:
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02.30.Yy
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(Control theory)
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42.50.Lc
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(Quantum fluctuations, quantum noise, and quantum jumps)
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| Fund: 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). |
Corresponding Authors:
Jie Wen, Jianchao Zeng
E-mail: wenjie015@gmail.com;zengjianchao@263.net
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Cite this article:
Jie Wen(温杰), Fangmin Wang(王芳敏), Yuanhao Shi(史元浩), Jianfang Jia(贾建芳), and Jianchao Zeng(曾建潮) Rapid stabilization of stochastic quantum systems in a unified framework 2023 Chin. Phys. B 32 070203
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