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借助Lyapunov方法的量子系统平衡态的布居控制

匡森,  丛爽

文章导航 > 自动化学报  > 2010 >  36(9): 1257-1263
匡森, 丛爽. 借助Lyapunov方法的量子系统平衡态的布居控制. 自动化学报, 2010, 36(9): 1257-1263. doi: 10.3724/SP.J.1004.2010.01257
引用本文: 匡森, 丛爽. 借助Lyapunov方法的量子系统平衡态的布居控制. 自动化学报, 2010, 36(9): 1257-1263. doi: 10.3724/SP.J.1004.2010.01257
shu
KUANG Sen, CONG Shuang. Population Control of Equilibrium States of Quantum Systems via Lyapunov Method. ACTA AUTOMATICA SINICA, 2010, 36(9): 1257-1263. doi: 10.3724/SP.J.1004.2010.01257
Citation: KUANG Sen, CONG Shuang. Population Control of Equilibrium States of Quantum Systems via Lyapunov Method. ACTA AUTOMATICA SINICA, 2010, 36(9): 1257-1263. doi: 10.3724/SP.J.1004.2010.01257
shu

借助Lyapunov方法的量子系统平衡态的布居控制

doi: 10.3724/SP.J.1004.2010.01257
  • 1.

    Department of Automation, University of Science and Technology of China, Hefei 230027, P.R. China

  • 2.

    Hefei National Laboratory for Physical Sciences at the Microscale, Hefei 230026, P.R. China

详细信息
    通讯作者:

    匡森

Population Control of Equilibrium States of Quantum Systems via Lyapunov Method

  • 1.

    Department of Automation, University of Science and Technology of China, Hefei 230027, P.R. China;

  • 2.

    Hefei National Laboratory for Physical Sciences at the Microscale, Hefei 230026, P.R. China

More Information
    Corresponding author: KUANG Sen

    摘要
  • 摘要: This paper studies the population control problem associated with the equilibrium states of mixed-state quantum systems by using a Lyapunov function with degrees of freedom. The control laws are designed by ensuring the monotonicity of the Lyapunov function; main results on the largest invariant set in the sense of LaSalle are given; and the strict expression of any state in the largest invariant set is normally deduced in the framework of Bloch vectors. By analyzing the obtained largest invariant set and the Lyapunov function itself, this paper also discusses the determination problem of the degrees of freedom. Numerical simulation experiments on a three-level system show the validity of research results.
    Abstract: This paper studies the population control problem associated with the equilibrium states of mixed-state quantum systems by using a Lyapunov function with degrees of freedom. The control laws are designed by ensuring the monotonicity of the Lyapunov function; main results on the largest invariant set in the sense of LaSalle are given; and the strict expression of any state in the largest invariant set is normally deduced in the framework of Bloch vectors. By analyzing the obtained largest invariant set and the Lyapunov function itself, this paper also discusses the determination problem of the degrees of freedom. Numerical simulation experiments on a three-level system show the validity of research results.
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出版历程
  • 收稿日期:  2009-11-23
  • 修回日期:  2010-03-17
  • 刊出日期:  2010-09-20

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