Quantum state estimation with minimal structured neural networks and its performance comparison
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.
neural networksquantum state estimationstructural optimization
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