# Accelerating lattice quantum Monte Carlo simulation using artificial neural networks: an application to the Holstein model

## TL;DR

This paper introduces neural network-enhanced Monte Carlo methods that significantly speed up simulations of the Holstein model by learning effective models, enabling faster and scalable lattice quantum Monte Carlo computations.

## Contribution

The authors develop neural network-based local and global move strategies for lattice Monte Carlo simulations, achieving substantial speedups and broad applicability to quantum and classical models.

## Key findings

- Neural networks accurately reproduce MC configuration weights.
- Achieved an order of magnitude speedup over traditional DQMC.
- Applicable to various classical and quantum lattice MC algorithms.

## Abstract

Monte Carlo (MC) simulations are essential computational approaches with widespread use throughout all areas of science. We present a method for accelerating lattice MC simulations using fully connected and convolutional artificial neural networks that are trained to perform local and global moves in configuration space, respectively. Both networks take local spacetime MC configurations as input features and can, therefore, be trained using samples generated by conventional MC runs on smaller lattices before being utilized for simulations on larger systems. This new approach is benchmarked for the case of determinant quantum Monte Carlo (DQMC) studies of the two-dimensional Holstein model. We find that both artificial neural networks are capable of learning an unspecified effective model that accurately reproduces the MC configuration weights of the original Hamiltonian and achieve an order of magnitude speedup over the conventional DQMC algorithm. Our approach is broadly applicable to many classical and quantum lattice MC algorithms.