Seeding neural network quantum states with tensor network states

Solving quantum many-body problems is one of the most challenging tasks in modern physics, and tensor network states have been widely used to efficiently represent quantum many-body states in recent years. Matrix product states (MPSs) [1-10], often specialized in one spatial dimension, and their generalizations to higher dimensions, such as projected entangled pair states (PEPSs) [9-14] and tree tensor networks [15-18], have been successfully applied to various quantum many-body problems in low-dimensional quantum systems by keeping the entanglement entropy of the wave function as low as possible. The number of variational parameters in tensor network states remains relatively small and grows only polynomially with the number of sites in most of quantum many-body systems. Recently, neural network quantum states (NNQSs) have been proposed as a new class of variational wave functions for quantum many-body systems [19-26]. One of the basic NNQSs is the restricted Boltzmann machine (RBM) wave function [19, 27-38].