Adaptive quantum circuits—where a quantum many-body state is controlled using measurements and conditional unitary operations—are a powerful paradigm for state preparation and quantum error-correction tasks. They can support two types of nonequilibrium quantum phase transitions: measurement-induced transitions between volume- and area-law-entangled steady states and control-induced transitions where the system falls into an absorbing state or, more generally, an orbit visiting several absorbing states. Within this context, nonlocal conditional operations can alter the critical properties of the two transitions and the topology of the phase diagram. Here, we consider the scenario where the measurements are , in order to engineer efficient control onto dynamical trajectories. Motivated by Rydberg-atom arrays, we consider a locally constrained model with global sublattice magnetization measurements and local correction operations to steer the system’s dynamics onto a many-body orbit with finite recurrence time. The model has a well-defined classical limit, which we leverage to aid our analysis of the control transition. As a function of the density of local correction operations, we find control and entanglement transitions with continuously varying critical exponents. For sufficiently high densities of local correction operations, we find that both transitions acquire a dynamical critical exponent z < 1 , reminiscent of criticality in long-range power-law interacting systems. At low correction densities, we find that the criticality reverts to a short-range nature with z ≳ 1 . In the long-range regime, the control and entanglement transitions are indistinguishable to within the resolution of our finite-size numerics, while in the short-range regime we find evidence that the transitions become distinct. We conjecture that the effective long-range criticality mediated by collective measurements is essential in driving the two transitions together.
Adaptive quantum circuits—where a quantum many-body state is controlled using measurements and conditional unitary operations—are a powerful paradigm for state preparation and quantum error-correction tasks. They can support two types of nonequilibrium quantum phase transitions: measurement-induced transitions between volume- and area-law-entangled steady states and control-induced transitions where the system falls into an absorbing state or, more generally, an orbit visiting several absorbing states. Within this context, nonlocal conditional operations can alter the critical properties of the two transitions and the topology of the phase diagram. Here, we consider the scenario where the measurements are , in order to engineer efficient control onto dynamical trajectories. Motivated by Rydberg-atom arrays, we consider a locally constrained model with global sublattice magnetization measurements and local correction operations to steer the system’s dynamics onto a many-body orbit with finite recurrence time. The model has a well-defined classical limit, which we leverage to aid our analysis of the control transition. As a function of the density of local correction operations, we find control and entanglement transitions with continuously varying critical exponents. For sufficiently high densities of local correction operations, we find that both transitions acquire a dynamical critical exponent z < 1 , reminiscent of criticality in long-range power-law interacting systems. At low correction densities, we find that the criticality reverts to a short-range nature with z ≳ 1 . In the long-range regime, the control and entanglement transitions are indistinguishable to within the resolution of our finite-size numerics, while in the short-range regime we find evidence that the transitions become distinct. We conjecture that the effective long-range criticality mediated by collective measurements is essential in driving the two transitions together.
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.
Monitored quantum circuits in which entangling unitary dynamics compete with projective local measurements can host measurement-induced phase transitions witnessed by entanglement measures at late times. Adding feedback conditioned on the measurement outcomes gives rise to another type of phase transition witnessed by local order parameters and correlation functions. These transitions, known as control or absorbing-state transitions, generically occur within the area-law entanglement phase and are thought to be governed by classical physics in that their critical exponents match those of the classical limit of the model. In this work, we examine quantum features of these transitions, focusing on a Bernoulli circuit model with a well-defined classical limit, in the presence of unitary dynamics, measurements, and feedback. First we demonstrate that, in the local basis defined by the absorbing state, the steady-state quantum coherence undergoes a phase transition at the control transition, where its logarithm changes discontinuously from volume- to area-law scaling. Second, we analyze the control transition from the perspective of fluctuations in observables, which carry two contributions: classical fluctuations over circuit realizations (present in the classical limit), and quantum fluctuations over trajectories and states (both absent in the classical limit). Both contributions can be estimated in experiments without post-selection. The circuit-to-circuit fluctuations, the dominant contribution, carry the critical behavior of the classical limit. However, the subleading quantum fluctuations that represent fluctuations between different quantum ``worlds'' also go critical at the control transition. These critical quantum fluctuations at the control transition also occur in other models, and we discuss how they can be measured experimentally without post-selection.
Mid-circuit measurements and feedback operations conditioned on the measurement outcomes are essential for implementing quantum error-correction on quantum hardware. When integrated in quantum many-body dynamics, they can give rise to novel non-equilibrium phase transitions both at the level of each individual quantum trajectory and the averaged quantum channel. Experimentally resolving both transitions on realistic devices has been challenging due to limitations on the fidelity and the significant latency for performing mid-circuit measurements and feedback operations in real time. Here, we develop a superconducting quantum processor that enables global mid-circuit measurement with an average quantum non-demolition (QND) fidelity of 98.7% and fast conditional feedback with a 200 ns real-time decision latency. Using this platform, we demonstrate the coexistence of an absorbing-state transition in the quantum channel and a measurement-induced entanglement transition at the level of individual quantum trajectories. For the absorbing-state transition, we experimentally extract a set of critical exponents at the transition point, which is in excellent agreement with the directed percolation universality class. Crucially, the two transitions occur at distinct values of the tuning parameter. Our results demonstrate that adaptive quantum circuits provide a powerful platform for exploring non-equilibrium quantum many-body dynamics.
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.
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 explore the dynamical phases of unitary Clifford circuits with variable-range interactions, coupled to a monitoring environment. We investigate two classes of models, distinguished by the action of the unitary gates, which either are organized in clusters of finite-range two-body gates, or are pair-wise interactions randomly distributed throughout the system with a power-law distribution. We find the range of the interactions plays a key role in characterizing both phases and their measurement-induced transitions. For the cluster unitary gates we find a transition between a phase with volume-law scaling of the entanglement entropy and a phase with area-law entanglement entropy. Our results indicate that the universality class of the phase transition is compatible to that of short range hybrid Clifford circuits. Oppositely, in the case of power-law distributed gates, we find the universality class of the phase transition changes continuously with the parameter controlling the range of interactions. In particular, for intermediate values of the control parameter, we find a non-conformal critical line which separates a phase with volume-law scaling of the entanglement entropy from one with sub-extensive scaling. Within this region, we find the entanglement entropy and the logarithmic negativity present a cross-over from a phase with algebraic growth of entanglement with system size, and an area-law phase.