Study On Deep Learning-Based Quantum State Tomography

Quantum state tomography plays a crucial role in quantum information processing.Developing deep learning-based quantum state tomography schemes has become a hot research topic in recent years.This dissertation focuses on the problem of developing high-fidelity quantum state tomography schemes in the presence of noisy and missing measurement values,mainly including the following three aspects.1.A quantum state tomography scheme based on the deep complex convolutional neural network(DC-CNN)is presented,to solve the problem of quantum state tomography subjected to missing measurement values.This scheme includes four steps.1)The density matrices are generated randomly and measured by using Pauli operators,and the corresponding measurement values are obtained.2)Measurement values are taken as input samples and density matrices as output samples,to form the dataset of the training samples.3)The architecture of the DC-CNN is designed,and optimized by the complex convolution attention mechanism.4)The DC-CNN is trained and tested,and then the network outputs are projected to the nearest subspace satisfying quantum state constraints to obtain the reconstructed density matrices.Simulation results reveal that the proposed scheme can achieve a higher fidelity compared with quantum state tomography schemes based on maximum likelihood estimation(MLE)and least square estimation(LSE).2.A quantum state tomography based on the U-net model and its variants,to deal with the problem of high-dimensional quantum state tomography subjected to both noisy and missing measurement values.This scheme includes four steps.1)The density matrices are generated randomly,and measured by Pauli operators,and the corresponding measurement values are obtained.2)Measurement values are taken as input samples,and Cholesky decompositions of the generated density matrices are performed to obtain the corresponding lower triangular matrices of output samples.3)Architectures of the U-net model and its variants are designed,where the variants include the RU-net with residual blocks,the AU-net with the attention mechanism,and the RAU-net with an improved combination of both.4)The U-net model and its variants are trained and tested,and the density matrices satisfying quantum state constraints are reconstructed by the inverse of the Cholesky decomposition after obtaining the lower triangular matrices of the network output.Compared with the quantum state tomography schemes based on the fully-connected network(FCN)and MLE,it is demonstrated that the proposed scheme can achieve a higher fidelity in the presence of noisy and missing measurement values for the tomography of high-dimensional quantum states.3.The question of whether and when deep learning methods outperform conventional optimization algorithms for quantum state tomography are answered,by presenting a comparison of four typical quantum state tomography schemes.The restricted Boltzmann machine network and the FCN are designed to perform state tomography for 2-qubit(low-dimensional)and 5-qubit(high-dimensional)states.The above two deep learning-based quantum state tomography schemes are compared with those based on MLE and LSE,where performance indicators are selected as fidelity,time cost and the number of parameters.Performance of low and high dimensional quantum state tomography under complete and incomplete measurement are compared as the number of measurement copies changes.Finally,applicable conditions of different schemes are given.