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arXiv:2304.09833 · PRX Quantum

Onset of Scrambling as a Dynamical Transition in Tunable-Range Quantum Circuits

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

Published Aug 23, 2023• 5 citations
arXivHTMLPDF

Abstract

In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size.This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes.In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity.In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior.We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space.This mapping predicts mean-field critical exponents ν = -1/(1 + s c ), which are consistent with the critical exponents extracted from Clifford-circuit numerics.In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.

DOI
10.1103/prxquantum.4.030325

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In a fast-scrambling many-body quantum system, information is spread and entanglement is built up on a time scale that grows logarithmically with the system size.This is of fundamental interest in understanding the dynamics of many-body systems, as well as in efficiently producing entangled resource states and error-correcting codes.In this work, we identify a dynamical transition marking the onset of scrambling in quantum circuits with different levels of long-range connectivity.In particular, we show that as a function of the interaction range for circuits of different structures, the tripartite mutual information exhibits a scaling collapse around a critical point between two clearly defined regimes of different dynamical behavior.We study this transition analytically in a related long-range Brownian-circuit model and show how the transition can be mapped onto the statistical mechanics of a long-range Ising model in a particular region of parameter space.This mapping predicts mean-field critical exponents ν = -1/(1 + s c ), which are consistent with the critical exponents extracted from Clifford-circuit numerics.In addition to systems with conventional power-law interactions, we identify the same phenomenon in deterministic sparse circuits that can be realized in experiments with neutral-atom arrays.
Long-range interactions in many-body quantum systems give rise to a wide range of dynamical phenomena, from collective dynamics well described by integrable mean-field models with symmetric all-to-all couplings, to fast scrambling of quantum information from disordered long-range interactions. Here, we investigate scenarios in which both regimes emerge within a single deterministic, translation-invariant XY spin model with long-range couplings. We consider a sparse powers-of-two (PWR2) graph, where each spin interacts with a logarithmic number of neighbors, and a power-law-decaying model. By altering the initial state via local perturbations on a completely symmetric state, we show that the dynamics changes from collective to scrambling as witnessed by bipartite and multipartite entanglement measures. We characterize this collective-to-scrambling crossover using Lyapunov exponents in the semiclassical regime, and show that the spectral properties of the coupling graph adjacency matrix provide a very efficient tool to predict the onset of fast scrambling. Our results offer a unified framework for controlling the switch between collective and scrambling dynamics in a setup accessible in experiments with neutral atoms in cavities or in tweezer arrays.
The competition between scrambling unitary evolution and projective measurements leads to a phase transition in the dynamics of quantum entanglement. Here, we demonstrate that the nature of this transition is fundamentally altered by the presence of long-range, power-law interactions. For sufficiently weak power laws, the measurement-induced transition is described by conformal field theory, analogous to short-range-interacting hybrid circuits. However, beyond a critical power law, we demonstrate that long-range interactions give rise to a continuum of nonconformal universality classes, with continuously varying critical exponents. We numerically determine the phase diagram for a one-dimensional, long-range-interacting hybrid circuit model as a function of the power-law exponent and the measurement rate. Finally, by using an analytic mapping to a long-range quantum Ising model, we provide a theoretical understanding for the critical power law.
We study how the information flows in many-body dynamics governed by random quantum circuits and discover a rich set of dynamical phase transitions in this information flow.The phase-transition points and their critical exponents are established across Clifford and Haar random circuits through finite-size scaling.The flow of both classical and quantum information, measured respectively by Holevo and coherent information, shows similar dynamical phase transition behaviors.We investigate how the phase transitions depend on the initial location of the information and the final probe region, and find ubiquitous behaviors in these transitions, revealing interesting properties about the information propagation and scrambling in this quantum many-body model.Our paper underscores rich behaviors of the information flow in large systems with numerous phase transitions, thereby sheds light on the understanding of quantum many-body dynamics.
Measurement-only circuits provide a minimal setting in which repeated local projections can either generate or suppress many-body entanglement, giving rise to measurement-induced phase transitions and dynamical regimes, that might have no unitary counterpart. Here we investigate entanglement and information transitions in one-dimensional measurement-only Clifford circuits with long-range two-qubit parity checks. By tuning both the measurement range and density per layer, we uncover a broad set of phases whose classification requires probes beyond entanglement entropy, such as mutual information, tripartite mutual information, purification from an ancilla, and Bell-cluster statistics. We map phase diagrams using large-scale Clifford simulations for two protocols: a random-basis design in which each measurement is randomly chosen from {XX,YY,ZZ}\lbrace XX,YY,ZZ \rbrace{XX,YY,ZZ}, and a single-basis design in which the basis is fixed within each layer but varies between layers, hence introducing more structure to the circuit. We map the trajectory-averaged entanglement entropy to a two-dimensional statistical mechanics model by extending a replica-based method to random-basis measurement-only circuits, and show that a continuous-time limit yields an effective long-range XX hamiltonian in the steady state. This connection links the observed volume-law to sub-volume-law entanglement transition to the boundary between a continuous symmetry broken phase and a critical XY phase. Strikingly, in structured (single-basis) circuits we find a phase in which volume-law and long-range entanglement coexists with rapid, size-independent purification of an ancilla qubit, and the absence of scrambling, highlighting measurement-only circuits as a promising route to efficiently preparing highly entangled and technologically useful quantum states.
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.
Information scrambling is nowadays one of the most important topics in various fields of research. Measurement-only circuits (MoCs) exhibit specific information scrambling dynamics, depending on the types of projective measurements and their mutual anticommutativity. The spatial range of the projective measurements in MoCs gives significant influences on circuit dynamics. In this work, we introduce and study long-range MoCs, which exhibit an interesting behavior in their dynamics. In particular, the long-range measurements can induce volume-law phases in MoCs without unitary time evolution, which come from anticommutative frustration of measurements specific to the long-range MoCs. This phenomenon occurs even in MoCs composed of solely two-body measurements, and it accompanies an entanglement phase transition. Crucially, our numerics find evidences that MoCs can be a fast scrambler. Interplay of high anticommutativity among measurements and their long-range properties generates fast entanglement growth in the whole system beyond linear-light-cone spreading.