Gauge Equivariant Neural Networks for 2+1D U(1) Gauge Theory Simulations in Hamiltonian Formulation

TL;DR

This paper introduces gauge equivariant neural networks for simulating 2+1D U(1) lattice gauge theories in Hamiltonian form, improving ground state approximations especially in strong coupling regimes.

Contribution

The paper develops gauge equivariant neural network wave functions for continuous-variable lattice gauge theories, advancing quantum simulation techniques.

Findings

Improved ground state energy estimates in strong coupling regimes.

Comparable results to existing methods in weak coupling regimes.

Demonstrated effectiveness of neural networks in gauge theory simulations.

Abstract

Gauge Theory plays a crucial role in many areas in science, including high energy physics, condensed matter physics and quantum information science. In quantum simulations of lattice gauge theory, an important step is to construct a wave function that obeys gauge symmetry. In this paper, we have developed gauge equivariant neural network wave function techniques for simulating continuous-variable quantum lattice gauge theories in the Hamiltonian formulation. We have applied the gauge equivariant neural network approach to find the ground state of 2+1-dimensional lattice gauge theory with U(1) gauge group using variational Monte Carlo. We have benchmarked our approach against the state-of-the-art complex Gaussian wave functions, demonstrating improved performance in the strong coupling regime and comparable results in the weak coupling regime.