Quantum State Estimation Based on Deep Learning LDAMP Networks

A learned denoising-based approximate message passing (LDAMP) deep learning network is proposed and trained in this paper, which is applied to the estimation of quantum states. This network combines denoising convolutional neural network with denoising-based approximate message passing algorithm. Using the measured output of the quantum system as the network input, the original density matrix was reconstructed by the designed LDAMP network with denoising convolutional neural network, and the structural features of various density matrices were extracted from a large number of training samples to realize the estimation of superposition and mixed states of quantum eigenstates. In the specific examples of quantum state estimation of four qubits, we study the performance of the quantum state estimation based on the LDAMP networks in the absence and presence of measurement interference, respectively, and compare the estimation performance with other algorithms which is based on compressed sensing such as alternating direction multiplier method and block matching 3D AMP. The numerical simulation results show that the LDAMP network can simultaneously estimate the four quantum states with higher accuracy in a small number of measurements. © 2023 Science Press. All rights reserved.