# General Methods for Digital Quantum Simulation of Gauge Theories

## TL;DR

This paper introduces a general framework for simulating gauge theories with matter fields on digital quantum computers, ensuring gauge invariance and demonstrating the approach on small lattice models including non-Abelian theories.

## Contribution

It develops a gauge-symmetry-preserving Trotterized evolution scheme and provides a method to obtain gauge-invariant operators for digital quantum simulation.

## Key findings

- Successfully simulated a 2+1D non-Abelian gauge theory on small lattices.
- Presented a gauge-invariant Trotterized time-evolution operator.
- Outlined procedures applicable to a broad class of gauge theories.

## Abstract

A general scheme is presented for simulating gauge theories, with matter fields, on a digital quantum computer. A Trotterized time-evolution operator that respects gauge symmetry is constructed, and a procedure for obtaining time-separated, gauge-invariant operators is detailed. We demonstrate the procedure on small lattices, including the simulation of a 2+1D non-Abelian gauge theory.