基于卷积神经网络的高效量子态层析方法  

Efficient quantum state tomography method based on convolutional neural networks

作　　者：孙乾[1] 蒋楠 SUN Qian;JIANG Nan(Department of Physics,Beijing Normal University,Beijing,China)

机构地区：[1]北京师范大学物理学系,北京

出　　处：《北京师范大学学报（自然科学版）》2024年第3期325-330,共6页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(12204055)。

摘　　要：通过系统梳理多种量子态层析技术的重构算法,并结合MATLAB数值模拟,比较并分析了线性重构与回归估计、极大似然估计,以及基于深度神经网络量子态层析方法的重构效果.结果表明:基于卷积神经网络重构算法在1~3量子比特时,能够用较短时间均实现>99.5%的保真度;相较于其他经典重构算法,基于卷积神经网络重构算法在算法复杂度及保真度上具有显著优势;又因其对复杂模型具有较好的拟合能力,且辅助解决了估计密度矩阵中出现负本征值的问题,使得重构所得估计密度矩阵全部具有物理意义.Various reconstruction algorithms of quantum state tomography are sorted out systematically.Combining with MATLAB numerical simulation,the reconstruction effects of linear reconstruction,linear regression estimation,maximum likelihood estimation and deep neural network-based quantum state tomography are compared and analyzed.For 1 to 3 qubits,convolutional neural network(CNN)based reconstruction algorithms achieves a fidelity of>99.5%with a shorter period of time,which has significant advantages in algorithm complexity and fidelity compared to other classical reconstruction algorithms.Due to the strong fitting ability to complex models,CNN helps to solve the problem of negative eigenvalues in estimated density matrices,making all the estimated density matrices reconstructed with it physically meaningful.

关 键 词：量子态层析 密度矩阵 卷积神经网络 保真度 负本征值 

分 类 号：O413.1[理学—理论物理]