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Fast Scrambling in a Long-range XX/YY/ZZ Measurement-only Quantum Circuit

Hinata Yokoyama

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

This study explores fast scrambling and measurement-induced phase transitions in long-range XX/YY/ZZ measurement-only quantum circuits. Using the stabilizer formalism and Gottesman-Knill theorem, we analyze entanglement growth, quantum information scrambling, and phase transitions in a one-dimensional spin-1/2 chain. The results reveal a transition from area-law to volume-law entanglement at a critical probability Pyy=0.185 for alpha=2.00, validated by finite-size scaling analysis. The initial state dependence and the role of long-range measurements are also examined. These findings enhance our understanding of non-equilibrium quantum dynamics and provide insights into their connection with fast scrambling and black hole analogies.

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This study explores fast scrambling and measurement-induced phase transitions in long-range XX/YY/ZZ measurement-only quantum circuits. Using the stabilizer formalism and Gottesman-Knill theorem, we analyze entanglement growth, quantum information scrambling, and phase transitions in a one-dimensional spin-1/2 chain. The results reveal a transition from area-law to volume-law entanglement at a critical probability Pyy=0.185 for alpha=2.00, validated by finite-size scaling analysis. The initial state dependence and the role of long-range measurements are also examined. These findings enhance our understanding of non-equilibrium quantum dynamics and provide insights into their connection with fast scrambling and black hole analogies.
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.
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.
We analyze the dynamics of entanglement entropy in a generic quantum many-body open system from the perspective of quantum information and error corrections. We introduce a random unitary circuit model with intermittent projective measurements, in which the degree of information scrambling by the unitary and the rate of projective measurements are independently controlled. This model displays two stable phases, characterized by the volume-law and area-law scaling entanglement entropy in steady states. The transition between the two phases is understood from the point of view of quantum error correction: the chaotic unitary evolution protects quantum information from projective measurements that act as errors. A phase transition occurs when the rate of errors exceeds a threshold that depends on the degree of information scrambling. We confirm these results using numerical simulations and obtain the phase diagram of our model. Our work shows that information scrambling plays a crucial role in understanding the dynamics of entanglement in an open quantum system and relates the entanglement phase transition to changes in quantum channel capacity.
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.
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.
The presence of quantum noises inherent to real physical systems can strongly impact the physics in hybrid quantum circuits with local random unitaries and midcircuit measurements. The quantum noises with a size-independent occurring probability can lead to the disappearance of a measurement-induced entanglement phase transition and the emergence of a single area-law phase. In this work, we investigate the effects of quantum noises with size-dependent probabilities $q=p/{L}^{\ensuremath{\alpha}}$, where $\ensuremath{\alpha}$ represents the scaling exponent. We have identified a noise-induced entanglement phase transition from a volume law to a power (area) law in the presence (absence) of measurements as ppp increases when $\ensuremath{\alpha}=1$. With the help of an effective statistical model, we reveal that the phase transition is of first order arising from the competition between two types of spin configurations and shares the same analytical understanding as the noise-induced coding transition. This unified picture further deepens the understanding of the connection between entanglement behavior and the capacity of information protection. When $\ensuremath{\alpha}\ensuremath{\ne}1$, one spin configuration always dominates regardless of ppp and thus the phase transition disappears. Moreover, we highlight the difference between the effects of size-dependent bulk noise and boundary noises. We validate our analytical predictions with extensive numerical results from stabilizer circuit simulations.