Measurement-induced phase transitions in sparse nonlocal scramblers

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.

arXiv comment11 pages, 6 figures (plus 11 page supplement with 11 figures)

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• Entanglement Transitions from Stochastic Resetting of Non-Hermitian Quasiparticles
• Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains
• Controlling entanglement at absorbing state phase transitions in random circuits
• Disordered monitored free fermions
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Universal KPZ scaling in noisy hybrid quantum circuits
• Criticality of quantum energy teleportation at phase transition points in quantum field theory
• Tunable Geometries in Sparse Clifford Circuits
• Measurement-induced criticality in extended and long-range unitary circuits