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Global stabilization control of stochastic quantum systems

随机量子系统的全局稳定控制

Abstract

The global stabilization control of arbitrary eigenstates for finite dimensional stochastic quantum systems with non-diagonal free Hamiltonian and non-regular measurement operator is studied in this paper. We propose a switching feedback control law, in which a constant control is used to steer the system state to a convergence domain, and another control law designed based on Lyapunov stability theorem, is used to attract the states in the convergence domain to the desired target state. The convergence to an arbitrary target eigenstate from any initial state is strictly proved. Moreover, numerical simulation experiments on a three-dimensional stochastic quantum system are implemented to demonstrate the effectiveness of the proposed control.

概要

中文概要

研究了对具有非对角自由哈密顿量以及非规则测量算符的有限维随机量子系统任意本征态控制的全局稳定性. 提出了一种开关反馈控制律, 其中一个常量控制用来驱动系统状态到收敛域中; 另一个基于李雅谱诺夫稳定性定理设计出的控制律被用来吸引状态到收敛域中的期望目标态. 严格证明了从任意初始态到任意目标本征态的收敛性, 并且通过3维随机量子系统的数值仿真实验展现了所提控制方法的有效性.

创新点

  1. 1)

    首次对具有非对角自由哈密顿量以及非规则测量算符的有限维随机量子系统采用李普诺夫控制理论进行了研究;

  2. 2)

    成功地推导出非规则的有限维随机量子系统任意本征态的全局稳定控制律, 并给出了严格证明;

  3. 3)

    所提出的控制方法简单、易于实现; 由所采用的控制理论所获得的控制律函数能够确保量子控制系统的状态以概率1转移并稳定到期望的目标状态, 对实际量子系统实验中调控性能的进一步提高具有重要意义.

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Author information

Correspondence to Shuang Cong.

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Cite this article

Cong, S., Wen, J., Kuang, S. et al. Global stabilization control of stochastic quantum systems. Sci. China Inf. Sci. 59, 112502 (2016). https://doi.org/10.1007/s11432-015-0911-7

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Keywords

  • eigenstate
  • stochastic quantum systems
  • global stabilization
  • switching control
  • Lyapunov stability theorem

关键词

  • 本征态
  • 随机量子系统
  • 全局稳定
  • 开关控制
  • 收敛性