Quantum control based on three forms of Lyapunov functions

doi:10.1088/1674-1056/ad11e6

中国物理B ›› 2024, Vol. 33 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/ad11e6

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Quantum control based on three forms of Lyapunov functions

Guo-Hui Yu(俞国慧) and Hong-Li Yang(杨洪礼)^†

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

收稿日期:2023-09-19 修回日期:2023-11-21 接受日期:2023-12-04 出版日期:2024-03-19 发布日期:2024-04-01
通讯作者: Hong-Li Yang E-mail:yhlmath@126.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 62176140).

Quantum control based on three forms of Lyapunov functions

Guo-Hui Yu(俞国慧) and Hong-Li Yang(杨洪礼)^†

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China

Received:2023-09-19 Revised:2023-11-21 Accepted:2023-12-04 Online:2024-03-19 Published:2024-04-01
Contact: Hong-Li Yang E-mail:yhlmath@126.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 62176140).

摘要/Abstract

摘要： This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors. In this paper, the specific control laws under the three forms are given. Stability is analyzed by the LaSalle invariance principle and the numerical simulation is carried out in a 2D test system. The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm. Finally, a unified form of the control laws under the three forms is given.

关键词: quantum system, Lyapunov function, particle swarm optimization, simulated annealing algorithms, quantum control

Abstract: This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state errors. In this paper, the specific control laws under the three forms are given. Stability is analyzed by the LaSalle invariance principle and the numerical simulation is carried out in a 2D test system. The calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing algorithm. Finally, a unified form of the control laws under the three forms is given.

Key words: quantum system, Lyapunov function, particle swarm optimization, simulated annealing algorithms, quantum control

中图分类号: (Ordinary differential equations)

02.30.Hq

03.65.-w (Quantum mechanics) 03.65.Aa (Quantum systems with finite Hilbert space)

Guo-Hui Yu(俞国慧) and Hong-Li Yang(杨洪礼). Quantum control based on three forms of Lyapunov functions[J]. 中国物理B, 2024, 33(4): 40201-040201.

Guo-Hui Yu(俞国慧) and Hong-Li Yang(杨洪礼). Quantum control based on three forms of Lyapunov functions[J]. Chin. Phys. B, 2024, 33(4): 40201-040201.

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Quantum control based on three forms of Lyapunov functions

Quantum control based on three forms of Lyapunov functions

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