Restricted-Boltzmann-Machine Learning for Solving Strongly Correlated Quantum Systems

TL;DR

This paper introduces a hybrid machine learning approach combining restricted Boltzmann machines with variational Monte Carlo to accurately solve strongly correlated quantum systems, outperforming previous methods.

Contribution

It develops a novel combined method that enhances the accuracy of quantum many-body simulations for spin and fermionic models on lattices.

Findings

Significant accuracy improvements over individual methods

Effective application to Heisenberg and Hubbard models

Proven as a powerful quantum many-body solver

Abstract

We develop a machine learning method to construct accurate ground-state wave functions of strongly interacting and entangled quantum spin as well as fermionic models on lattices. A restricted Boltzmann machine algorithm in the form of an artificial neural network is combined with a conventional variational Monte Carlo method with pair product (geminal) wave functions and quantum number projections. The combination allows an application of the machine learning scheme to interacting fermionic systems. The combined method substantially improves the accuracy beyond that ever achieved by each method separately, in the Heisenberg as well as Hubbard models on square lattices, thus proving its power as a highly accurate quantum many-body solver.