# Deep Learning-Enhanced Variational Monte Carlo Method for Quantum Many-Body Physics

## TL;DR

This paper introduces an efficient deep neural network approach with a new optimization algorithm to accurately compute ground states in quantum many-body systems, demonstrating significant speed and accuracy improvements.

## Contribution

The paper presents a novel importance sampling gradient optimization algorithm and an efficient convolutional DNN architecture for quantum many-body calculations.

## Key findings

- Achieved ground-state energies matching exact solutions for 1D SU(N) spin chains.
- Demonstrated improved training speed for deep neural networks in VMC.
- Successfully computed loop correlation functions using the trained wave functions.

## Abstract

Artificial neural networks have been successfully incorporated into variational Monte Carlo method (VMC) to study quantum many-body systems. However, there have been few systematic studies of exploring quantum many-body physics using deep neural networks (DNNs), despite of the tremendous success enjoyed by DNNs in many other areas in recent years. One main challenge of implementing DNN in VMC is the inefficiency of optimizing such networks with large number of parameters. We introduce an importance sampling gradient optimization (ISGO) algorithm, which significantly improves the computational speed of training DNN in VMC. We design an efficient convolutional DNN architecture to compute the ground state of a one-dimensional (1D) SU($N$) spin chain. Our numerical results of the ground-state energies with up to 16 layers of DNN show excellent agreement with the Bethe-Ansatz exact solution. Furthermore, we also calculate the loop correlation function using the wave function obtained. Our work demonstrates the feasibility and advantages of applying DNNs to numerical quantum many-body calculations.