Real-time simulation of (2+1)-dimensional lattice gauge theory on qubits

TL;DR

This paper demonstrates real-time quantum simulation of a 2+1 dimensional Z2 lattice gauge theory using qubits, addressing gauge redundancy and charge conservation, with results from both noiseless and noisy quantum hardware.

Contribution

It introduces a dual variable formulation to reduce gauge degrees of freedom and resolves artificial charge unconservation in quantum simulations.

Findings

Successful simulation of real-time evolution with static charges

Comparison of noiseless simulator and real hardware results

Addressed gauge redundancy and charge conservation issues

Abstract

We study the quantum simulation of Z2 lattice gauge theory in 2+1 dimensions. The dual variable formulation, the so-called Wegner duality, is utilized for reducing redundant gauge degrees of freedom. The problem of artificial charge unconservation is resolved for any charge distribution. As a demonstration, we simulate the real-time evolution of the system with two static electric charges, i.e., with two temporal Wilson lines. Some results obtained by the simulator (with no hardware noise) and the real device (with sizable hardware noise) of a quantum computer are shown.