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n比特随机量子系统实时状态估计及其反馈控制

张骄阳 丛爽 匡森

张骄阳, 丛爽, 匡森. n比特随机量子系统实时状态估计及其反馈控制. 自动化学报, 2022, 48(x): 1−12 doi: 10.16383/j.aas.c210916
引用本文: 张骄阳, 丛爽, 匡森. n比特随机量子系统实时状态估计及其反馈控制. 自动化学报, 2022, 48(x): 1−12 doi: 10.16383/j.aas.c210916
Zhang Jiao-Yang, Cong Shuang, Kuang Sen. Real-time state estimation and feedback control for n-qubit stochastic quantum systems. Acta Automatica Sinica, 2022, 48(x): 1−12 doi: 10.16383/j.aas.c210916
Citation: Zhang Jiao-Yang, Cong Shuang, Kuang Sen. Real-time state estimation and feedback control for n-qubit stochastic quantum systems. Acta Automatica Sinica, 2022, 48(x): 1−12 doi: 10.16383/j.aas.c210916

n比特随机量子系统实时状态估计及其反馈控制

doi: 10.16383/j.aas.c210916
基金项目: 国家自然科学基金(61973290)资助
详细信息
    作者简介:

    张骄阳:中国科学技术大学自动化系硕士研究生. 2020年获得中国海洋大学自动化专业学士学位. 主要研究方向为基于Lyapunov方法的量子控制, 量子噪声抑制. E-mail: jyzhang98@mail.ustc.edu.cn

    丛爽:中国科学技术大学自动化系教授. 1995年获得意大利罗马大学系统工程博士学位. 主要研究方向为运动控制中的先进控制策略, 模糊逻辑控制, 神经网络设计与应用, 机器人协调控制和量子系统控制. 本文通信作者. E-mail: scong@ustc.edu.cn

    匡森:中国科学技术大学自动化系副教授. 2007年获得中国科学技术大学控制理论与控制工程专业博士学位. 主要研究方向为量子信息与控制, 量子人工智能, 智能控制及其应用. E-mail: skuang@ustc.edu.cn

Real-time State Estimation and Feedback Control for n-qubit Stochastic Quantum Systems

Funds: Supported by National Natural Science Foundation of China (61973290)
More Information
    Author Bio:

    ZHANG Jiao-Yang Master student in the Department of Automation, University of Science and Technology of China. He received his bachelor degree in automation from Ocean University of China in 2020. His research interest covers Lyapunov-based quantum control and quantum noise suppression

    CONG Shuang Professor in the Department of Automation, University of Science and Technology of China. She received her Ph. D. degree in system engineering from the University of Rome “La Sapienza”, Rome, Italy, in 1995. Her research interest covers advanced control strategies for motion control, fuzzy logic control, neural networks design and applications, robotic coordination control, and quantum systems control. Corresponding author of this paper

    KUANG Sen Associate professor in the Department of Automation, University of Science and Technology of China. He received his Ph. D. degree in control theory and control engineering from University of Science and Technology of China in 2007. His research interest covers quantum information and control, quantum artificial intelligence, and intelligent control and its applications

  • 摘要: 对于连续弱测量过程存在高斯噪声的情况, 基于在线交替方向乘子法推导出一种适用于n比特随机量子系统实时状态估计的算法QSE-OADM; 运用李雅普诺夫方法设计控制律, 实现基于实时量子状态估计的反馈控制, 并证明所提控制律的收敛性. 以2比特随机量子系统为例进行数值仿真实验, 通过与基于QST-OADM算法和OPG-ADMM算法的实时量子状态估计及其反馈控制方案的性能对比, 显示出所提控制方案的优越性.
  • 图  1  不同外部控制场的作用下的实时状态估计性能

    Fig.  1  Real-time state estimation performance under various external control fields

    图  2  不同初始测量算符作用下的实时状态估计性能

    Fig.  2  Real-time state estimation performance under various initial measurement operators

    图  3  不同的相互作用强度作用下的实时状态估计性能

    Fig.  3  Real-time state estimation performance under various interaction strengths

    图  4  第30次采样时2比特量子系统估计状态与真实状态比较 ($ H' = {H_0} + {\;}1\cdot{\sigma _x} $, $ {M_1} = {\sigma _z} \otimes {\sigma _z} $, $ L' = {\;}0.7{\sigma _z} $)

    Fig.  4  Comparison between the estimated state and the real state of a 2-qubit system at the 30th sampling time ($ H' = {H_0} + {\;}1\cdot{\sigma _x} $, $ {M_1} = {\sigma _z} \otimes {\sigma _z} $, $ L' = {\;}0.7{\sigma _z} $)

    图  5  基于实时状态估计的n比特随机量子系统反馈控制方案的框图

    Fig.  5  Real-time state estimation-based feedback control scheme for n-qubit stochastic quantum systems

    图  6  实时量子状态估计性能及本征态反馈控制的实验结果

    Fig.  6  Experimental results of real-time quantum state estimation performance and eigenstate feedback control

    图  7  实时量子状态估计性能及叠加态反馈控制的实验结果

    Fig.  7  Experimental results of real-time quantum state estimation performance and superposition state feedback control

    表  1  测量值序列的构造方法

    Table  1  Construction approach of the measurement record sequence

    $y_1$$y_2$$ \cdots $$y_k$
    $b_1$${\rm{tr}}(M_1^\dagger {\rho _1})$$ \cdots $
    $b_2$${\rm{tr}}(M_2^\dagger {\rho _2})$${\rm{tr}}(M_1^\dagger {\rho _2})$$ \cdots $
    $\vdots$$\vdots$$\vdots$$ \vdots $$\vdots$
    $b_k$${\rm{tr}}(M_k^\dagger {\rho _k})$${\rm{tr}}(M_{k - 1}^\dagger {\rho _k})$$\cdots$${\rm{tr}}(M_1^\dagger {\rho _k})$
    下载: 导出CSV

    表  2  本征态反馈控制性能指标的对比

    Table  2  Comparison of performance indicators of eigenstate feedback control

    方案1方案2方案3
    $k_{s1}$141825
    $k_{s2}$151828
    $Fidelity$(30)99.84%99.40%98.29%
    $V(30)$$5.399 \times {10^{ - 4}}$$1.484 \times {10^{ - 3}}$$6.312 \times {10^{ - 3}}$
    $J(30)$18.24728.72152.112
    下载: 导出CSV

    表  3  叠加态反馈控制性能指标的对比

    Table  3  Comparison of performance indicators of superposition state feedback control

    方案1方案2方案3
    $k_{s1}$162229
    $k_{s2}$162533
    $Fidelity$(40)99.90%99.40%98.30%
    $V(40)$$1.651 \times {10^{ - 4}}$$6.180 \times {10^{ - 4}}$$2.854 \times {10^{ - 3}}$
    $J(40)$133.179133.880136.223
    下载: 导出CSV
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  • 收稿日期:  2021-09-26
  • 录用日期:  2022-06-06
  • 网络出版日期:  2022-07-18

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