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Bulletin of the American Physical Society

Measurement-induced phase transitions in deterministic non-local quantum circuits

Tomohiro Hashizume, Gregory S. Bentsen, Andrew J. Daley

Published Mar 19, 2021• 0 citations
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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.
We study multiparty entanglement near measurement induced phase transitions (MIPTs), which arise in ensembles of local quantum circuits built with unitaries and measurements. In contrast to equilibrium quantum critical transitions, where entanglement is short-ranged, MIPTs possess long-range k-party genuine multiparty entanglement (GME) characterized by an infinite hierarchy of entanglement exponents for k ≥ 2. First, we represent the average spread of entanglement with "entanglement clusters", and use them to conjecture general exponent relations: 1) classical dominance, 2) monotonicity, 3) subadditivity. We then introduce measure-weighted graphs to construct such clusters in general circuits. Second, we obtain the exact entanglement exponents for a 1d MIPT in a measurement-only circuit that maps to percolation by exploiting non-unitary conformal field theory. The exponents, which we numerically verify, obey the inequalities. We also extend the construction to a 2d MIPT that maps to classical 3d percolation, and numerically find the first entanglement exponents. Our results provide a firm ground to understand the multiparty entanglement of MIPTs, and more general ensembles of quantum circuits.
We study one-dimensional hybrid quantum circuits perturbed by quenched quasiperiodic (QP) modulations across the measurement-induced phase transition (MIPT). Considering non-Pisot QP structures, characterized by unbounded fluctuations, allows us to tune the wandering exponent $\ensuremath{\beta}$ to exceed the Luck bound $\ensuremath{\nu}\ensuremath{\ge}1/(1\ensuremath{-}\ensuremath{\beta})$ for the stability of the MIPT, where $\ensuremath{\nu}=1.28(2)$. Via robust numerical simulations of random Clifford circuits interleaved with local projective measurements, we find that sufficiently large QP structural fluctuations destabilize the MIPT and induce a flow to a broad family of critical dynamical phase transitions of the infinite QP type that is governed by the wandering exponent $\ensuremath{\beta}$. We numerically determine the associated critical properties, including the correlation length exponent consistent with saturating the Luck bound, and a universal activated dynamical scaling with activation exponent $\ensuremath{\psi}\ensuremath{\cong}\ensuremath{\beta}$, finding excellent agreement with the conclusions of real-space renormalization group calculations.