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arXiv:2208.10506

Revealing measurement-induced phase transitions by pre-selection

Michael Buchhold, Thomas J. Mueller, Sebastian Diehl

Published Sep 16, 2022• 14 citations
arXivHTMLPDF

Abstract

Abstract Pushing forward the understanding of general non-unitary dynamics in controlled quantum platforms has been fueled by the recent discovery of measurement-induced phases and phase transitions. So far, these transi- tions remained largely elusive, since they are masked in standard quantum mechanical observables due to the randomness of measurement outcomes. Here, we establish a general scheme – pre-selection – to make them observable: The outcome randomness is broken explicitly by steering the system towards a representative state, which corresponds to one out of exponentially many possible measurement outcomes. Remarkably, this steer- ing can be chosen so gently that the basic properties of the underlying measurement-induced transition, such as entanglement structure and critical exponents, are not modified. Pre-selection introduces a unique dark or absorbing state with macroscopic order, replacing the maximally mixed stationary state of the unconditioned measurement trajectory ensemble. This creates a link of measurement-induced phase transitions to new forms of quantum absorbing state transitions, which can be detected by standard means via a local order parameter. This insight further enables a quantum simulation strategy, determining the underlying universality class in state-of-the-art quantum platforms without measurement readout.

DOI
10.21203/rs.3.rs-2019123/v1

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Abstract Pushing forward the understanding of general non-unitary dynamics in controlled quantum platforms has been fueled by the recent discovery of measurement-induced phases and phase transitions. So far, these transi- tions remained largely elusive, since they are masked in standard quantum mechanical observables due to the randomness of measurement outcomes. Here, we establish a general scheme – pre-selection – to make them observable: The outcome randomness is broken explicitly by steering the system towards a representative state, which corresponds to one out of exponentially many possible measurement outcomes. Remarkably, this steer- ing can be chosen so gently that the basic properties of the underlying measurement-induced transition, such as entanglement structure and critical exponents, are not modified. Pre-selection introduces a unique dark or absorbing state with macroscopic order, replacing the maximally mixed stationary state of the unconditioned measurement trajectory ensemble. This creates a link of measurement-induced phase transitions to new forms of quantum absorbing state transitions, which can be detected by standard means via a local order parameter. This insight further enables a quantum simulation strategy, determining the underlying universality class in state-of-the-art quantum platforms without measurement readout.
Nascent quantum computers motivate the exploration of quantum many-body systems in nontraditional scenarios. For example, it has become natural to explore the dynamics of systems evolving under both unitary evolution and measurement. Such systems can undergo dynamical phase transitions in the entanglement properties of quantum trajectories conditional on the measurement outcomes. Here, we explore dynamics in which one attempts to (locally) use those measurement outcomes to steer the system toward a target state, and we study the resulting phase diagram as a function of the measurement and feedback rates. Steering succeeds when the measurement and feedback rates exceed a threshold, yielding an absorbing-state transition in the trajectory-averaged density matrix. We argue that the absorbing-state transition generally occurs at different critical parameters from the entanglement transition in individual trajectories and has distinct critical properties. The efficacy of steering depends on the nature of the target state: in particular, for local dynamics targeting long-range correlated states, steering is necessarily slow and the entanglement and steering transitions are well separated in parameter space.
Information-theoretic phase transitions, such as the measurement-induced phase transition (MIPT), characterize the robustness of quantum dynamics to local monitoring and are naturally formulated in terms of trajectories conditioned on typical measurement outcomes, which are naively accessible only through postselection. Here, we implement forced measurements to investigate how explicit postselection alters the nature of the transition. We find that postselection fundamentally alters the universality class by reweighting trajectories that are otherwise rare. In particular, we obtain a correlation-length exponent ν≈2.1ν\approx 2.1ν≈2.1 larger than that of the standard MIPT and a negative effective central charge ceff≈−0.35c_\mathrm{eff}\approx -0.35ceff​≈−0.35. We also compare the postselected MIPT to the entanglement transition of random tensor networks, and demonstrate that their universality class is the same. This setup further allows time-periodic, translationally invariant circuits with postselected weak measurements. In both models, we find that an on-site dimension of at least 3 (qutrits but not qubits) is necessary to induce a transition.
We explore universality and phases of matter in hybrid quantum dynamics combining chaotic time evolution and projective measurements.We develop a unitary representation of measurements based on the Stinespring theorem, which we crucially identify with the time evolution of the system and measurement apparatus, affording significant technical advantages and conceptual insight into hybrid dynamics.We diagnose spectral properties in the presence of measurements for the first time, along with standard, experimentally tractable probes of phase structure, finding no nontrivial effects due to measurements in the absence of feedback.We also establish that nonlinearity in the density matrix is neither sufficient nor necessary to see a transition, and instead identify utilization of the measurement outcomes (i.e., "feedback") as the crucial ingredient.After reviewing the definition of a phase of matter, we identify nontrivial orders in adaptive hybrid dynamics-in which measurement outcomes determine future unitary gates-finding a genuine measurement-induced absorbing-state phase transition in an adaptive quantum East model.In general, we find that only deterministic and constrained Haar-random dynamics with active feedback and without continuous symmetries can realize genuine, measurement-induced phases of matter.
Measurement-induced entanglement phase transitions in monitored quantum circuits have stimulated activity in a diverse research community. However, the study of measurement-induced dynamics, due to the requirement of exponentially complex postselection, has been experimentally limited to small or specially designed systems that can be efficiently simulated classically. We present a solution to this outstanding problem by introducing a scalable protocol in U(1)U(1)U(1) symmetric circuits that facilitates the observation of entanglement phase transitions \emph{directly} from experimental data, without detailed assumptions of the underlying model or benchmarking with simulated data. Thus, the method is applicable to circuits which do not admit efficient classical simulation and allows a reconstruction of the full entanglement entropy curve with minimal theoretical input. Our approach relies on adaptive circuits and a steering protocol to approximate pure-state trajectories with mixed ensembles, from which one can efficiently filter out the subsystem U(1)U(1)U(1) charge fluctuations of the target trajectory to obtain its entanglement entropy. The steering protocol replaces the exponential costs of postselection and state tomography with a scalable overhead which, for fixed accuracy εεε and circuit size LLL, scales as Ns∼L5/2/ε\mathcal{N}_s\sim L^{5/2}/εNs​∼L5/2/ε.
One of the main postulates of quantum mechanics is that measurements destroy quantum coherence (wave function collapse). Recently it was discovered that in a many-body system dilute local measurements still preserve some coherence across the entire system. As the measurement density is increased, a phase transition occurs that is characterized by the disentanglement of different parts of the system. Unfortunately, this transition is impossible to observe experimentally for macroscopic systems because it requires an exponentially costly full tomography of the many-body wave function or a comparison with the simulation on an oracle classical computer. In this work we report the discovery of another measurement-induced phase transition that can be observed experimentally if quantum dynamics can be reversed. On one side of this phase transition the quantum information encoded in some part of the Hilbert space is fully recovered after the time inversion. On the other side, all quantum information is corrupted. This transition also manifests itself as the change in the behavior of the probability to observe the same measurement outcome in the process that consists of identical blocks repeated many times. In each block the unitary evolution is followed by the measurement. On one side of the transition the probability decreases exponentially with the number of repetitions, on the other it tends to a constant as the number of repetitions is increased. We confirm the existence of the proposed phase transition through numerical simulations of realistic quantum circuits and analytical calculations using an effective random-matrix theory model.
Thanks to recent experimental advances in simulating and detecting quantum dynamics with high precision and controllability, our understanding of the physics of monitored quantum systems has considerably deepened over the past decades. In this article, we provide an introductory theoretical review on the basic formalisms governing open quantum dynamics under measurement, along with recent developments in their spectral and typical aspects. After reviewing quantum measurement theory, we introduce the concept of quantum trajectories, which are the conditional dynamics of monitored states shaped by a set of measurement outcomes. We then discuss the spectral properties of the dynamical map describing the evolution averaged over measurement outcomes. As has recently been recognized, these spectral features are intimately connected to whether quantum trajectories exhibit typical behaviors, such as ergodicity and purification. Moreover, we introduce Lyapunov exponents of typical quantum trajectories and discuss how these quantities serve as indicators of measurement-induced phase transitions in monitored quantum many-body systems.