A minimal implementation of Yang-Mills theory on a digital quantum computer

TL;DR

This paper introduces a simplified, resource-efficient implementation of SU(N) Yang-Mills theory on digital quantum computers, with improvements for convergence and benchmarking against Monte Carlo simulations.

Contribution

It presents new simplified Hamiltonians and methods to enhance convergence, supporting practical quantum simulation of non-Abelian gauge theories.

Findings

Reduced resource requirements for SU(2) implementation.

Validated analytical improvements with Monte Carlo benchmarks.

Supports noncompact-variable approach for quantum simulation.

Abstract

We present a minimal implementation of SU($N$) pure Yang-Mills theory in $3+1$ dimensions for digital quantum simulation, designed to enable quantum advantage. Building on the orbifold lattice simulation protocol with logarithmic scaling in the local Hilbert-space truncation, we introduce further simplified Hamiltonians. Furthermore, we test simple methods that improve the convergence to the infinite mass limit, thereby removing the requirement of a large scalar mass to obtain the Kogut-Susskind Hamiltonian. For the SU(2) theory, we can cut the resource requirement further by utilizing the embedding of $\mathrm{SU}(2)\cong\mathrm{S}^3$ into $\mathbb{R}^4$. Monte Carlo simulations of the Euclidean path integral were used to benchmark the accuracy of these new analytical improvements to the theory. These results provide further support for the noncompact-variable-based approach as a practical framework for quantum simulation of non-Abelian gauge theories.