SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers

TL;DR

This paper presents an improved method for simulating one-dimensional SU(2) non-Abelian gauge theories on quantum computers, reducing unphysical states and enhancing circuit efficiency, demonstrated through multi-plaquette calculations on IBM hardware.

Contribution

It introduces a new mapping that minimizes unphysical states and leverages gauge symmetry for more efficient quantum simulations of SU(2) gauge theories.

Findings

Reduced unphysical Hilbert space in the mapping

Efficient quantum circuits exploiting gauge symmetry

Successful multi-plaquette simulation on IBM hardware

Abstract

An improved mapping of one-dimensional SU(2) non-Abelian gauge theory onto qubit degrees of freedom is presented. This new mapping allows for a reduced unphysical Hilbert space. Insensitivity to interactions within this unphysical space is exploited to design more efficient quantum circuits. Local gauge symmetry is used to analytically incorporate the angular momentum alignment, leading to qubit registers encoding the total angular momentum on each link. The results of a multi-plaquette calculation on IBM's quantum hardware are presented.