Measurement-induced phase transitions in sparse nonlocal scramblers

TL;DR

This paper explores measurement-induced phase transitions in fast scramblers with sparse nonlocal interactions, revealing their enhanced resilience to measurements and potential for robust quantum error correction.

Contribution

It introduces a class of sparse nonlocal circuits that interpolate between local and fully nonlocal systems, demonstrating their superior measurement resilience and error-correcting capabilities.

Findings

Sparse nonlocal circuits withstand higher measurement rates.

Maximally nonlocal circuits support nearly extensive code distance.

Sparse circuits offer pathways for noise-resilient quantum computing.

Abstract

Measurement-induced phase transitions arise due to a competition between the scrambling of quantum information in a many-body system and local measurements. In this work we investigate these transitions in different classes of fast scramblers, systems that scramble quantum information as quickly as is conjectured to be possible -- on a timescale proportional to the logarithm of the system size. In particular, we consider sets of deterministic sparse couplings that naturally interpolate between local circuits that slowly scramble information and highly nonlocal circuits that achieve the fast-scrambling limit. We find that circuits featuring sparse nonlocal interactions are able to withstand substantially higher rates of local measurement than circuits with only local interactions, even at comparable gate depths. We also study the quantum error-correcting codes that support the volume-law entangled phase and find that our maximally nonlocal circuits yield codes with nearly extensive contiguous code distance. Use of these sparse, deterministic circuits opens pathways towards the design of noise-resilient quantum circuits and error correcting codes in current and future quantum devices with minimum gate numbers.