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arXiv:2210.07256 · PRX Quantum

Measurement-Induced Phases of Matter Require Feedback

Aaron J. Friedman, Oliver Hart, Rahul Nandkishore

Published Oct 13, 2023• 34 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/prxquantum.4.040309

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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.
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.
We show how distinct phases of matter can be generated by performing random single-qubit measurements on a subsystem of toric code. Using a parton construction, such measurements map to random Gaussian tensor networks, and in particular, random Pauli measurements map to a classical loop model in which watermelon correlators precisely determine measurement-induced entanglement. Measuring all but a 1d boundary of qubits realizes hybrid circuits involving unitary gates and projective measurements in 1+11+11+1 dimensions. We find that varying the probabilities of different Pauli measurements can drive transitions in the unmeasured boundary between phases with different orders and entanglement scaling, corresponding to short- and long-loop phases in the classical model. Furthermore, by utilizing single-site boundary unitaries conditioned on the bulk measurement outcomes, we generate mixed-state ordered phases and transitions that can be experimentally diagnosed via linear observables. This demonstrates how parton constructions provide a natural framework for measurement-based quantum computing setups to produce and manipulate phases of matter.
We provide an overview of standard "projective" quantum measurements with the goal of elucidating connections between theory and experiment. We make use of a unitary "Stinespring" representation of measurements on a dilated Hilbert space that includes both the physical degrees of freedom and those of the measurement apparatus. We explain how this unitary representation (i) is guaranteed by the axioms of quantum mechanics, (ii) relates to both the Kraus and von Neumann representations, and (iii) corresponds to the physical time evolution of the system and apparatus during the measurement process. The Stinespring representation also offers significant conceptual insight into measurements, helps connects theory and experiment, is particularly useful in describing protocols involving midcircuit measurements and outcome-dependent operations, and establishes that all quantum operations are compatible with relativistic locality, among other insights.
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.
Probing a quantum system disrupts its state in a phenomenon known as backaction. In this work we investigate the conditions for this disruption to result in a phase transition in the information dynamics of a monitored system. We introduce a framework that captures a wide range of experiments encompassing probes comprised of projective measurements and probes which more generally transfer quantum information from the system to a quantum computer. The latter case is relevant to the recently introduced quantum-enhanced experiments in which quantum postprocessing is performed on a quantum computer and which can offer an exponential sampling advantage over projective measurements and classical postprocessing. Our framework explicitly considers the effects of an environment using a model of unitary evolution which couples the system, apparatus, and environment. Information dynamics is investigated using the R\'enyi and von Neumann entropies of the evolving state, and we construct a replica theory for studying these quantities. We identify the possible replica symmetries an experiment can possess and discuss the meaning of their spontaneous symmetry breaking. In particular, we identify a minimum subgroup whose spontaneous symmetry breaking results in an entanglement transition. This symmetry is only possible when the information in the apparatus is as informative about the dynamics of the system as the information transferred to the environment. We call this requirement the information exchange symmetry and quantify it by a relationship between the entropies. We then introduce a generalized notion of spontaneous symmetry breaking such that the entanglement transition can be understood as the spontaneous breaking of the information exchange symmetry and without referring to the replica theory. Information exchange symmetry breaking is then shown to generalize the phenomenology of the measurement-induced phase transition (MIPT). We apply this theory to a quantum-enhanced experiment probing the unitary dynamics of a Haar brickwork quantum circuit, and we determine that the universality class of the critical point is distinct from that for the MIPT. This notion of information exchange symmetry breaking generalizes the MIPT and provides a framework for understanding the dynamics of quantum information in quantum-enhanced experiments.
Understanding how complex systems transition between order and chaos is a central challenge of nonequilibrium physics. While weak perturbations of classical integrable systems give rise to a mixed phase space of coexisting regular and chaotic trajectories, analogous behavior in interacting quantum many-body systems has remained elusive. Here we develop and experimentally implement a hybrid quantum-classical feedback protocol that autonomously discovers and stabilizes long-lived regular trajectories in a superconducting quantum processor. Each iteration combines short-time quantum evolution with classical optimization that projects the dynamics back onto a low-entanglement variational manifold, effectively distilling coherence from chaotic evolution. The stabilized trajectories reveal a quantum many-body mixed phase space emerging from nonlinear variational dynamics, without a direct analogue in classical or few-body quantum systems. Our results establish a versatile framework for algorithmic discovery and control of coherent dynamics previously inaccessible to experiment.