SU(2) lattice gauge theory on a quantum annealer

TL;DR

This paper demonstrates the implementation of SU(2) lattice gauge theory on a quantum annealer, showing potential for quantum hardware to contribute to non-Abelian gauge theory simulations.

Contribution

First exploration of SU(2) lattice gauge theory on a quantum annealer, using D-Wave hardware to compute eigenvalues, eigenvectors, and vacuum expectations.

Findings

Successful calculation of eigenvalues and eigenvectors

Observation of vacuum expectation values

Potential for quantum annealers in lattice gauge theory

Abstract

Lattice gauge theory is an essential tool for strongly interacting non-Abelian fields, such as those in quantum chromodynamics where lattice results have been of central importance for several decades. Recent studies suggest that quantum computers could extend the reach of lattice gauge theory in dramatic ways, but the usefulness of quantum annealing hardware for lattice gauge theory has not yet been explored. In this work, we implement SU(2) pure gauge theory on a quantum annealer for lattices comprising a few plaquettes in a row with a periodic boundary condition. These plaquettes are in two spatial dimensions and calculations use the Hamiltonian formulation where time is not discretized. Numerical results are obtained from calculations on D-Wave Advantage hardware for eigenvalues, eigenvectors, vacuum expectation values, and time evolution. The success of this initial exploration indicates that the quantum annealer might become a useful hardware platform for some aspects of lattice gauge theories.