最简结构神经网络的量子态估计及其性能对比

Quantum state estimation with minimal structured neural networks and its performance comparison

中文关键词  神经网络  量子态估计  结构优化

英文关键词  neural networks  quantum state estimation  structural optimization

中文摘要

      本文提出并设计两种具有最简结构的前向神经网络, 来高精度实现对量子态密度矩阵的估计. 训练出具有函数逼近功能的反向传播(BP)神经网络和径向基函数(RBF)网络进行量子密度矩阵估计的应用. 根据量子态密度矩阵与量子系统实验装置的输出测量值之间的关系, 建立并构造出训练神经网络的输入/输出样本对; 通过对网络的归一化处理, 获得满足量子密度矩阵条件的网络输出. 分别对2量子位的本征态、叠加态和混合态的估计设计和训练出不同网络, 并在给定的性能指标下, 与采用深度学习算法的具有两个隐含层的宽度网络(WNN)的量子密度矩阵估计性能进行对比分析. 在此基础上, 采用RBF神经网络对高量子位密度矩阵进行估计实验. 分别在最少隐含层节点数、最少训练样本数、最短训练时间, 以及对非样本输入数据的泛化能力方面, 通过仿真实验对所设计网络的量子密度矩阵估计的优越性能进行对比研究.

英文摘要

      In this paper, two feedforward neural networks with the minimal structure are proposed and designed to estimate the quantum state density matrix with high accuracy. The back propagation (BP) neural network and the radial basis function (RBF) with function approximation function are designed and trained for the application of quantum density matrix estimation. According to the relationship between the quantum state density matrix and the output measurement value of the quantum system experimental device of the quantum system, the input/output sample pairs for training the neural networks’ weights are established and constructed. The network output satisfying the condition of quantum density matrix is obtained by normalizing the networks. Different networks are designed and trained for 2-qubit eigenstate, superposition state and mixed state, and the performances of different networks are compared with the quantum density matrix estimation results of width neural network (WNN) with two hidden layers using deep learning algorithm under the same given performance index. On this basis, the RBF neural network is used to estimate the high qubit density matrix. The superior performances of the quantum density matrix estimation of the designed networks in the minimum number of hidden layer nodes, the minimum training samples, the minimum training time and the generalization ability of non-sample input data are compared by simulation experiments.