Introduction to the artificial neural network-based variational Monte Carlo method

TL;DR

This paper introduces a neural network-based variational Monte Carlo method for quantum state simulation, emphasizing the mathematical formulation, advantages, and applications to physical systems.

Contribution

It presents a novel approach combining neural networks with variational Monte Carlo, highlighting the method's formulation, benefits, and application examples.

Findings

Effective neural network trial wave functions for quantum systems

Stable optimization via the variational method as unsupervised learning

Successful application to Yukawa potential and hydrogen molecule

Abstract

The construction of trial wave functions based on neural networks combined with the variational Monte Carlo method is discussed. The mathematical formulation for representing quantum states as artificial neural networks is introduced. The advantages of employing such trial states and how machine learning works are discussed. It is shown that the variational method is a kind of unsupervised learning algorithm, where the multiple minima landscape is used as an asset that leads to a stable optimization procedure. The feature representation plays an important role on interpretability and on extracting physical insights from nontrivial trial wave functions. The algorithm is illustrated for the Yukawa potential and the hydrogen molecule.