Suppressing Gauge Drift in Quantum Simulations with Gauge Transformations

TL;DR

This paper presents a method to suppress gauge drift in quantum simulations of lattice gauge theories by combining frequent gauge transformations and the Zeno effect, demonstrated on a 1D SU(2) model.

Contribution

It introduces a novel approach using gauge transformations and the Zeno effect to maintain gauge invariance during quantum simulations.

Findings

Effective suppression of gauge drift demonstrated on a 1D SU(2) model.

Gauge transformations reduce unphysical state amplitudes.

Frequent projections help maintain physical subspace fidelity.

Abstract

The simulation of quantum lattice gauge theories faces the major challenge of maintaining gauge invariance, as various errors in the simulation push the state of the system out of the physical subspace of the system's exponentially larger Hilbert space. This paper outlines a method, based off of previous work, that uses gauge transformations in two ways. Firstly, the method exploits the Zeno effect by conducting frequent projections to suppress gauge drift. These projections utilize local gauge transformations to destructively interfere unphysical amplitudes via coupling to an ancillary qubit while the physical amplitudes are left untouched, up to a less than unity normalization factor. Secondly, gauge transformations are conducted throughout the time evolution of the system to hamper the speed of gauge drift. This paper demonstrates this method on a pure 1D SU$(2)$ toy model.