Investigating reconstruction of quantum state distributions with neural networks

In recent years, machine learning techniques are well used to promote quantum information research. Because of its flexibility and strong expressive ability, neural network can make it possible to approximate the optimal solutions of quantum information problems. In this paper, we investigate reconstruction of quantum state distributions (QSDs) using two popular generative models: variational autoencoder (VAE) and conditional variational autoencoder (CVAE). We discover that the Shannon entropy of QSD is suitable to evaluate the quality of reconstruction, and can be utilized to guide the research of other quantum information problems. We investigate the potential of CVAE in reconstruction of multiple QSDs. Experiment results show that CVAE can generally achieve comparable compression rate to that of VAE. If the QSDs are very similar, using CVAE to reconstruct them can greatly reduce the network size and save a lot of training time. Our experiment results also demonstrate that deeper networks do not necessarily lead to better reconstruction fidelity, and the number of network parameters grows linearly with respect to the number of qubits, although the dimension of QSD grows exponentially.