Suppression of $1/f$ noise in quantum simulators of gauge theories

TL;DR

This paper demonstrates that linear gauge protection effectively suppresses $1/f$ noise-induced gauge violations in quantum simulators of gauge theories, enhancing the fidelity of complex quantum simulations.

Contribution

It introduces and numerically validates a method to suppress decoherence errors caused by $1/f$ noise in gauge theory quantum simulators, supported by analytic derivations.

Findings

Linear gauge protection suppresses gauge violations as $1/V^eta$.

The method is effective for $ ext{U}(1)$ and $ ext{Z}_2$ lattice gauge theories.

Results are applicable to modern quantum simulation platforms.

Abstract

In the current drive to quantum-simulate evermore complex gauge-theory phenomena, it is necessary to devise schemes allowing for the control and suppression of unavoidable gauge-breaking errors on different experimental platforms. Although there have been several successful approaches to tackle coherent errors, comparatively little has been done in the way of decoherence. By numerically solving the corresponding Bloch--Redfield equations, we show that the recently developed method of \textit{linear gauge protection} suppresses the growth of gauge violations due to $1/f^\beta$ noise as $1/V^\beta$, where $V$ is the protection strength and $\beta>0$, in Abelian lattice gauge theories, as we show through exemplary results for $\mathrm{U}(1)$ quantum link models and $\mathbb{Z}_2$ lattice gauge theories. We support our numerical findings with analytic derivations through time-dependent perturbation theory. Our findings are of immediate applicability in modern analog quantum simulators and digital NISQ devices.