Observation of disorder-free localization using a (2+1)D lattice gauge theory on a quantum processor

TL;DR

This paper demonstrates disorder-free localization in a (2+1)D lattice gauge theory on a quantum processor, revealing localization without disorder and proposing a superposition-based sampling algorithm for quantum many-body systems.

Contribution

It introduces a novel approach to observe disorder-free localization using superpositions over gauge sectors in a lattice gauge theory on a quantum computer.

Findings

Localization occurs without disorder in 1D and 2D LGTs.

Superposition states differ from disorder-sampled states in entropy.

Proposed algorithm offers polynomial speedup in disorder sampling.

Abstract

Disorder-induced phenomena in quantum many-body systems pose significant challenges for analytical methods and numerical simulations at relevant time and system scales. To reduce the cost of disorder-sampling, we investigate quantum circuits initialized in states tunable to superpositions over all disorder configurations. In a translationally-invariant lattice gauge theory (LGT), these states can be interpreted as a superposition over gauge sectors. We observe localization in this LGT in the absence of disorder in one and two dimensions: perturbations fail to diffuse despite fully disorder-free evolution and initial states. However, R\'enyi entropy measurements reveal that superposition-prepared states fundamentally differ from those obtained by direct disorder sampling. Leveraging superposition, we propose an algorithm with a polynomial speedup in sampling disorder configurations, a longstanding challenge in many-body localization studies.