Artificial Intelligence for Quantum Matter: Finding a Needle in a Haystack

TL;DR

This paper introduces a scalable neural network approach to accurately model complex quantum many-body wave functions, enabling efficient simulations of large, entangled quantum systems with high precision.

Contribution

It presents a novel method for learning neural network representations of quantum states from probability densities, achieving high overlaps and facilitating large-scale quantum simulations.

Findings

Achieved up to 99.9% overlap with target wave functions.

Successfully simulated fractional quantum Hall states with 25 particles.

Uncovered edge features in quantum Hall systems.

Abstract

Neural networks (NNs) have great potential in solving the ground state of various many-body problems. However, several key challenges remain to be overcome before NNs can tackle problems and system sizes inaccessible with more established tools. Here, we present a general and efficient method for learning the NN representation of an arbitrary many-body complex wave function from its N-particle probability density and probability current density and successfully test on (non-Abelian) fractional quantum Hall states and chiral BCS wavefunction. Having reached overlaps as large as 99.9%, we employ our neural wave function for pre-training to effortlessly solve the fractional quantum Hall problem with Coulomb interactions and realistic Landau-level mixing for as many as 25 particles and uncover distinctive features of the edge. Our work demonstrates efficient, scalable and accurate simulation of highly-entangled quantum matter using general-purpose deep NNs enhanced with physics-informed initialization.