# Gluon Field Digitization for Quantum Computers

## TL;DR

This paper introduces a digitization scheme for $SU(3)$ gauge theories suitable for quantum computers, enabling accurate classical and potential quantum simulations of QCD with minimal qubits.

## Contribution

A novel digitization method using the subgroup $S(1080)$ for $SU(3)$ gauge theories, with a modified action allowing simulations in the scaling window.

## Key findings

- Classical Monte Carlo results match full $SU(3)$ continuum extrapolations.
- The digitization scheme achieves sub-percent precision at multiple lattice spacings.
- The method is suitable for NISQ-era quantum chromodynamics simulations.

## Abstract

Simulations of gauge theories on quantum computers require the digitization of continuous field variables. Digitization schemes that uses the minimum amount of qubits are desirable. We present a practical scheme for digitizing $SU(3)$ gauge theories via its discrete subgroup $S(1080)$. The $S(1080)$ standard Wilson action cannot be used since a phase transition occurs as the coupling is decreased, well before the scaling regime. We proposed a modified action that allows simulations in the scaling window and carry out classical Monte Carlo calculations down to lattice spacings of order $a\approx 0.08$ fm. We compute a set of observables with sub-percent precision at multiple lattice spacings and show that the continuum extrapolated value agrees with the full $SU(3)$ results. This suggests that this digitization scheme provides sufficient precision for NISQ-era QCD simulations.