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arXiv:2109.00013 · Physical review. B./Physical review. B

Entanglement phases in large- N hybrid Brownian circuits with long-range couplings

Subhayan Sahu, Shao-Kai Jian, Gregory S. Bentsen, Brian G. Swingle

Published Dec 9, 2022• 25 citations
arXivHTMLPDF

Abstract

The interplay of unitary gates and quantum measurements leads to quantum many-body states with unique patterns of entanglement, and can even drive phase transitions between distinct entanglement phases. Here, the authors construct analytically solvable models to study the effects of long-range coupling on such measurement-induced phases, and also provide a minimal theoretical understanding of the phases and the phase transition in both spin and fermionic models. They show that power law couplings and measurements result in a rich entanglement phase diagram, including robust dynamical quantum phases with good error correcting properties, namely a power-law code distance.

DOI
10.1103/physrevb.106.224305

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The interplay of unitary gates and quantum measurements leads to quantum many-body states with unique patterns of entanglement, and can even drive phase transitions between distinct entanglement phases. Here, the authors construct analytically solvable models to study the effects of long-range coupling on such measurement-induced phases, and also provide a minimal theoretical understanding of the phases and the phase transition in both spin and fermionic models. They show that power law couplings and measurements result in a rich entanglement phase diagram, including robust dynamical quantum phases with good error correcting properties, namely a power-law code distance.
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.
Measurements can drive quantum many-body systems into nontrivial steady states and induce interesting dynamical phase transitions, rendering measurement-only quantum circuits a useful platform for exploring quantum many-body phases beyond those of equilibrium Hamiltonian systems. Here we study a class of long-range measurement-only quantum circuits with competing two-qubit and three-qubit measurements. We demonstrate that these circuits exhibit rich steady-state structure and uncover a strong influence of the measurement range on the resulting phases. In particular, states with symmetry-protected topological (SPT) order can emerge with sufficiently short-range measurements beyond the nearest-neighbor limit. These states feature robust topological edge modes, which can also be detected from circuit dynamics. With longer-range measurements, an extended parameter regime emerges in which conventional order parameters are suppressed while spatial correlations remain nontrivial. Moreover, we show that in this circuit model sufficiently long-range measurements can produce significant entanglement with scaling beyond an area law despite the absence of any unitary evolution.
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.
Unitary circuits subject to repeated projective measurements can undergo an entanglement phase transition (EPT) as a function of the measurement rate.This transition is generally understood in terms of a competition between the scrambling effects of unitary dynamics and the disentangling effects of measurements.We find that, surprisingly, EPTs are possible even in the absence of scrambling unitary dynamics, where they are best understood as arising from measurements alone.This finding motivates us to introduce measurement-only models, in which the "scrambling" and "unscrambling" effects driving the EPT are fundamentally intertwined and cannot be attributed to physically distinct processes.These models represent a novel form of an EPT, conceptually distinct from that in hybrid unitary-projective circuits.We explore the entanglement phase diagrams, critical points, and quantum code properties of some of these measurement-only models.We find that the principle driving the EPTs in these models is frustration, or mutual incompatibility, of the measurements.Surprisingly, an entangling (volume-law) phase is the generic outcome when measuring sufficiently long but still local (≳3-body) operators.We identify a class of exceptions to this behavior ("bipartite ensembles") which cannot sustain an entangling phase but display dual area-law phases, possibly with different kinds of quantum order, separated by self-dual critical points.Finally, we introduce a measure of information spreading in dynamics with measurements and use it to demonstrate the emergence of a statistical light cone, despite the nonlocality inherent to quantum measurements.
Many-body unitary dynamics interspersed with repeated measurements display a rich phenomenology hallmarked by measurement-induced phase transitions. Employing feedback-control operations that steer the dynamics toward an absorbing state, we study the entanglement entropy behavior at the absorbing state phase transition. For short-range control operations, we observe a transition between phases with distinct subextensive scalings of entanglement entropy. In contrast, the system undergoes a transition between volume-law and area-law phases for long-range feedback operations. The fluctuations of entanglement entropy and of the order parameter of the absorbing state transition are fully coupled for sufficiently strongly entangling feedback operations. In that case, entanglement entropy inherits the universal dynamics of the absorbing state transition. This is, however, not the case for arbitrary control operations, and the two transitions are generally distinct. We quantitatively support our results by introducing a framework based on stabilizer circuits with classical flag labels. Our results shed new light on the problem of observability of measurement-induced phase transitions.
We investigate the distribution of entanglement entropy in hybrid quantum circuits consisting of random unitary gates and local measurements applied at a finite rate. We demonstrate that higher moments of the entanglement entropy distribution, such as the ratio between the variance and the mean and the skewness, capture nontrivial features of the measurement-induced dynamics that are invisible to the mean entropy alone. We demonstrate that these quantities exhibit distinct and robust behaviors across the volume-law and area-law phases, and can serve as effective diagnostics of measurement-induced entanglement transitions. We propose a phenomenological model describing the effect of measurements in the area-law regime, which, when combined with the directed polymer in a random environment description of the volume-law phase, well matches numerical simulations across the entire phase diagram.