基于李雅普诺夫控制的随机开放量子系统特性分析

丛爽; 胡龙珍; 薛静静; 温杰

doi:10.3981/j.issn.1000-7857.2014.22.001

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科技导报 ›› 2014, Vol. 32 ›› Issue (22) : 15-22. DOI: 10.3981/j.issn.1000-7857.2014.22.001

研究论文

基于李雅普诺夫控制的随机开放量子系统特性分析

作者信息 -

中国科学技术大学自动化系, 合肥230027

作者简介:

丛爽，教授，研究方向为先进控制策略、人工神经网络、智能控制及量子系统控制等，电子信箱：scong@ustc.edu.cn；胡龙珍（共同第一作者），硕士研究生，研究方向为开放量子系统的特性分析和状态控制，电子信箱：lzhzh1217@mail.ustc.edu.cn

Characteristic Analysis of Stochastic Open Quantum Systems via Lyapunov-based Control

Author information -

Department of Automation, University of Science and Technology of China, Hefei 230027, China

摘要

测量给确定性的开放量子系统带来了随机项，使随机开放量子系统本身产生一些马尔科夫和非马尔科夫开放量子系统所不具有的特性，这些特性给随机开放量子系统带来一些新的作用和影响。在目前有关随机开放量子系统李雅普诺夫控制理论研究的基础上，分别对无控制作用下随机开放量子系统的内部特性、开关控制和连续控制作用下系统的状态转移性能进行仿真研究。结果表明，在测量所带来的随机回馈项的作用下，在无控制的自由演化情况下，系统的状态最终随机地收敛到测量算符的某个本征态，其可能达到的本征态的个数与初态密度矩阵中对角线非零元素的个数相等；不论是开关控制还是连续控制，系统都能够从任意的初始纯态转移到期望的本征态，但相比于开关控制，连续控制的收敛速度更快，达到期望目标态所用时间更短。

Abstract

Quantum measurement brings a stochastic term to deterministic open quantum systems, which makes the systems display some unique characteristics distinguished from the Markovian and non-Markovian open quantum systems. These characteristics bring some new roles to and effect on the stochastic open quantum system. Based on the related work on the global stability for stochastic open quantum systems via Lyapunov stabilization theorem established recently, the characteristic analysis without control fields and the state transfer with the switching control and continuous control are studied, respectively. Numerical simulation experiments are implemented under the Matlab environment. The simulation results demonstrate that the system without the action of the control will randomly converge to some eigenstate of the measurement operator and the numbers of eigenstates and diagonal non-zero elements of the initial state's density matrix are equal, and that under the action of the control, the stochastic open quantum system can transfer the state from an arbitrary initial pure state to the desired target eigenstate.However, compared to the switching control, the continuous control system performance has a faster convergence speed and a shorter transfer time.

导出引用

丛爽, 胡龙珍, 薛静静, 温杰. 基于李雅普诺夫控制的随机开放量子系统特性分析[J]. 科技导报, 2014, 32(22): 15-22 https://doi.org/10.3981/j.issn.1000-7857.2014.22.001

CONG Shuang, HU Longzhen, XUE Jingjing, WEN Jie. Characteristic Analysis of Stochastic Open Quantum Systems via Lyapunov-based Control[J]. Science & Technology Review, 2014, 32(22): 15-22 https://doi.org/10.3981/j.issn.1000-7857.2014.22.001

中图分类号： TP202+.4

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