Zeno Effect Suppression of Gauge Drift in Quantum Simulations

TL;DR

This paper introduces a method using the Zeno effect to suppress gauge drift in quantum simulations of gauge theories, ensuring the system remains within the physical subspace during evolution.

Contribution

It proposes a Zeno effect-based approach with a technique to reduce gauge drift speed, improving gauge invariance preservation in quantum simulations.

Findings

Effective suppression of gauge drift demonstrated on a $\\mathbb{Z}_2$ gauge theory toy model.

Frequent projections onto the physical subspace help maintain gauge invariance.

Reducing the gauge drift speed decreases the frequency of required projections.

Abstract

Quantum simulation of lattice gauge theories is a promising tool for the study of many complicated problems including ones with real-time dynamics. For gauge theories, however, there is a major challenge in maintaining gauge invariance during time evolution. Such theories have a full Hilbert space that is larger than the physical space -- the set of states which are gauge invariant or equivalently respect the Gauss law. While an exact implementation of Hamiltonian dynamics starting in the physical Hilbert space will keep the system in the physical space, various types of errors will inevitably produce components outside of it. This work proposes a method of suppressing this gauge drift via the Zeno effect. As in the standard picture of the Zeno effect, our method relies on frequent projection onto the physical subspace. Additionally, a technique is discussed to reduce the speed of the gauge drift, which helps to reduce the required frequency of projections. We demonstrate our method on a $\mathbb{Z}_2$ gauge theory toy model.