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基于深度学习LDAMP网络的量子状态估计

林文瑞 丛爽

林文瑞, 丛爽. 基于深度学习LDAMP网络的量子状态估计. 自动化学报, 2021, x(x): 1−12 doi: 10.16383/j.aas.c210156
引用本文: 林文瑞, 丛爽. 基于深度学习LDAMP网络的量子状态估计. 自动化学报, 2021, x(x): 1−12 doi: 10.16383/j.aas.c210156
Lin Wen-Rui, Cong Shuang. Quantum state estimation based on deep learning LDAMP networks. Acta Automatica Sinica, 2021, x(x): 1−12 doi: 10.16383/j.aas.c210156
Citation: Lin Wen-Rui, Cong Shuang. Quantum state estimation based on deep learning LDAMP networks. Acta Automatica Sinica, 2021, x(x): 1−12 doi: 10.16383/j.aas.c210156

基于深度学习LDAMP网络的量子状态估计

doi: 10.16383/j.aas.c210156
基金项目: 国家自然科学基金(61973290, 61720106009)资助
详细信息
    作者简介:

    林文瑞:中国科学技术大学自动化系硕士研究生. 2019年获得中国科学技术大学自动化系学士学位. 主要研究方向为基于深度学习网络的量子状态估计. Email: lwryjj@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, 机器人协调控制以及量子系统控制. 本文通讯作者. Email: scong@ustc.edu.cn

Quantum State Estimation Based on Deep Learning LDAMP Networks

Funds: Supported by National Natural Science Foundation of P. R. China (61973290, 61720106009)
More Information
    Author Bio:

    LIN Wen-Rui Master student in the Department of Automation,University of Science and technology of China. He received his bachelor degree from Department of Automation,University of Science and technology of China in 2019. His research interest covers quantum state estimation based on deep learning networks

    CONG Shuang Professor in the Department of Automation, University of Science and Technology of China. She received her Ph. D. 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

  • 摘要: 本文设计出一种基于学习去噪的近似消息传递(Learned denoising-based approximate message passing, LDAMP)的深度学习网络, 将其应用于量子状态的估计. 该网络将去噪卷积神经网络(Denoising convolutional neural network, DnCNN)与基于去噪的近似消息传递(Denoising-based approximate message passing, DAMP)算法相结合, 利用量子系统输出的测量值作为网络输入, 通过设计出的带有DnCNN的LDAMP网络重构出原始密度矩阵, 从大量的训练样本中提取各种不同类型密度矩阵的结构特征, 来实现对量子本征态、叠加态以及混合态的估计. 在对4个量子位的量子态估计的具体实例中, 我们分别在无和有测量噪声干扰情况下, 对基于LDAMP网络的量子态估计进行了仿真实验性能研究, 并与基于压缩感知的交替方向乘子法(Alternating direction multiplier method, ADMM)和三维块匹配近似消息传递(Block matching 3D AMP, BM3D-AMP)等算法进行估计性能对比研究. 数值仿真实验结果表明, 所设计的LDAMP网络可以在较少的测量的采样率下同时完成对四种量子态的更高精度估计.
  • 图  1  LDAMP中第l级网络结构图

    Fig.  1  Structure of the l-level network in the LDAMP

    图  2  DnCNN降噪器的网络结构图

    Fig.  2  Network structure of the DnCNN denoiser

    图  3  DnCNN降噪器输入变量的尺寸变换过程

    Fig.  3  Size transformation process of input variable of the DnCNN denoiser

    图  4  DnCNN降噪器的MSE性能

    Fig.  4  MSE performance of the DnCNN denoiser

    图  5  LDAMP网络和其他方法的归一化距离性能对比(SNR=40 dB)

    Fig.  5  Comparison of normalized distance performance between LDAMP network and other methods with SNR=40 dB

    图  6  LDAMP网络对不同量子态密度矩阵估计的归一化距离性能对比

    Fig.  6  Comparison of normalized distance performance of LDAMP network for estimation of density matrices of different quantum states

    图  7  不同采样率下LDAMP网络的仿真和状态演化方程的MSE(dB)性能对比(SNR=40 dB)

    Fig.  7  Comparison of MSE(dB) performance between simulation and SE analysis of LDAMP network for different sampling ratios with SNR=40 dB

    图  8  对角混合态密度矩阵${{\boldsymbol{\rho}} _3}$的真实测量值与含噪声测量值对比($\eta = 0.1$)

    Fig.  8  Comparison of measured value between the real and the noisy of diagonal mixed state density matrix with $\eta = 0.1$

    图  9  对角混合态密度矩阵${{\boldsymbol{\rho}} _3}$及其在无和含测量噪声下估计矩阵的模值分布($\eta = 0.1$)

    Fig.  9  Diagonal mixed state density matrix and its modulus distribution of estimation matrix without and including measurement noise with $\eta = 0.1$

    图  10  不同采样率下LDAMP网络对四种量子态密度矩阵估计时的MSE性能

    Fig.  10  MSE performance of the LDAMP network for the estimation of four quantum state density matrices with different sampling ratios

    表  1  LDAMP网络和其他方法的MSE(dB)性能比较($\eta = 0.1$)

    Table  1  Comparison of MSE(dB) performance between LDAMP network and other methods with $\eta = 0.1$

    SNR01020304050607080无干扰
    LDAMP−25.7984−29.0129−32.8600−33.6109−36.0653−36.5386−38.0527−38.9837−40.0702−41.0905
    ADMM−14.6620−23.0837−30.2725−33.0952−34.5782−35.3161−35.4256−35.5693−35.9288−36.1332
    BM3D-AMP−24.8475−25.1181−25.3271−25.7576−26.2451−26.4625−26.7987−26.7337−26.9364−27.3626
    NLM-AMP−25.6457−25.2723−25.1595−25.3828−25.4296−25.5618−25.7596−25.9587−26.0826−26.2108
    Gauss-AMP−25.6424−25.6433−25.6620−25.6991−25.6728−25.6729−25.6786−25.6985−25.6940−25.7053
    Bilateral-AMP−25.1949−25.1813−25.1152−25.1163−25.1209−25.1663−25.2087−25.2193−25.2296−25.2332
    下载: 导出CSV
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  • 收稿日期:  2021-02-21
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