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.
Highlights
Measurement-induced phase transitions (MIPT) [1–4] are transitions driven by a competition between scrambling dynamics, which tends to generate many-body entanglement across all degrees of freedom of a quantum many-body system, and local measurements, which tend to destroy this entanglement
In this paper we explore these connections by studying how the strength of scrambling affects the properties of the MIPT mixed phase by considering sparsely-coupled quantum circuits with tunable nonlocal interactions
Our analysis demonstrates that sparse nonlocal interactions can significantly improve a quantum system’s robustness to local measurements
Summary
Measurement-induced phase transitions (MIPT) [1–4] are transitions driven by a competition between scrambling dynamics, which tends to generate many-body entanglement across all degrees of freedom of a quantum many-body system, and local measurements, which tend to destroy this entanglement. Random all-to-all circuits [43], and other disordered all-to-all coupled models such as the SYK model [44,45] are good examples of fast scramblers, but recently, a number of deterministic and experimentally feasible systems exhibiting fast scrambling have been explored [46–49] These show similar dynamics, but often on sparse nonlocal coupling graphs. In this paper we explore these connections by studying how the strength of scrambling affects the properties of the MIPT mixed phase by considering sparsely-coupled quantum circuits with tunable nonlocal interactions.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
