Measurement-induced phase transitions in sparse nonlocal scramblers

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