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                    基于深度學習LDAMP網絡的量子狀態估計

                    林文瑞 叢爽

                    林文瑞, 叢爽. 基于深度學習LDAMP網絡的量子狀態估計. 自動化學報, 2021, x(x): 1?12 doi: 10.16383/j.aas.c210156
                    引用本文: 林文瑞, 叢爽. 基于深度學習LDAMP網絡的量子狀態估計. 自動化學報, 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

                    基于深度學習LDAMP網絡的量子狀態估計

                    doi: 10.16383/j.aas.c210156
                    基金項目: 國家自然科學基金(61973290, 61720106009)資助
                    詳細信息
                      作者簡介:

                      林文瑞:中國科學技術大學自動化系碩士研究生. 2019年獲得中國科學技術大學自動化系學士學位. 主要研究方向為基于深度學習網絡的量子狀態估計. Email: lwryjj@mail.ustc.edu.cn

                      叢爽:中國科學技術大學自動化系教授. 1995年獲得意大利羅馬大學系統工程博士學位, 主要研究方向為運動控制中的先進控制策略, 模糊邏輯控制, 神經網絡設計與應用, 機器人協調控制以及量子系統控制. 本文通訊作者. 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: 本文設計出一種基于學習去噪的近似消息傳遞(Learned denoising-based approximate message passing, LDAMP)的深度學習網絡, 將其應用于量子狀態的估計. 該網絡將去噪卷積神經網絡(Denoising convolutional neural network, DnCNN)與基于去噪的近似消息傳遞(Denoising-based approximate message passing, DAMP)算法相結合, 利用量子系統輸出的測量值作為網絡輸入, 通過設計出的帶有DnCNN的LDAMP網絡重構出原始密度矩陣, 從大量的訓練樣本中提取各種不同類型密度矩陣的結構特征, 來實現對量子本征態、疊加態以及混合態的估計. 在對4個量子位的量子態估計的具體實例中, 我們分別在無和有測量噪聲干擾情況下, 對基于LDAMP網絡的量子態估計進行了仿真實驗性能研究, 并與基于壓縮感知的交替方向乘子法(Alternating direction multiplier method, ADMM)和三維塊匹配近似消息傳遞(Block matching 3D AMP, BM3D-AMP)等算法進行估計性能對比研究. 數值仿真實驗結果表明, 所設計的LDAMP網絡可以在較少的測量的采樣率下同時完成對四種量子態的更高精度估計.
                    • 圖  1  LDAMP中第l級網絡結構圖

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

                      圖  2  DnCNN降噪器的網絡結構圖

                      Fig.  2  Network structure of the DnCNN denoiser

                      圖  3  DnCNN降噪器輸入變量的尺寸變換過程

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

                      圖  4  DnCNN降噪器的MSE性能

                      Fig.  4  MSE performance of the DnCNN denoiser

                      圖  5  LDAMP網絡和其他方法的歸一化距離性能對比(SNR=40 dB)

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

                      圖  6  LDAMP網絡對不同量子態密度矩陣估計的歸一化距離性能對比

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

                      圖  7  不同采樣率下LDAMP網絡的仿真和狀態演化方程的MSE(dB)性能對比(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

                      圖  8  對角混合態密度矩陣${{\boldsymbol{\rho}} _3}$的真實測量值與含噪聲測量值對比($\eta = 0.1$)

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

                      圖  9  對角混合態密度矩陣${{\boldsymbol{\rho}} _3}$及其在無和含測量噪聲下估計矩陣的模值分布($\eta = 0.1$)

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

                      圖  10  不同采樣率下LDAMP網絡對四種量子態密度矩陣估計時的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網絡和其他方法的MSE(dB)性能比較($\eta = 0.1$)

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

                      SNR01020304050607080無干擾
                      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
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                    • 收稿日期:  2021-02-21
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