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.
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.
Programmable quantum hardware provides an emerging platform for exploring and controlling non-unitary quantum dynamics through measurement-based operations. In this work, we introduce feedback-directed circuit architectures that integrate spatially structured mid-circuit measurements with real-time conditional operations to steer the evolution of random dynamics, and perform their large-scale simulations (up to 100 qubits) on programmable digital quantum processors. By promoting measurement from a passive readout to an active control signal, these adaptive monitored circuits enable directional information flow and generate intrinsic asymmetry in random circuit simulations. We implement this framework on IBM superconducting quantum processors and observe robust, noise-resilient signatures of feedback-induced asymmetry distinct from the more well-known non-Hermitian skin effect. Our results establish feedback as a programmable resource for non-unitary control, opening new avenues for engineering measurement-based dynamics, non-equilibrium phenomena, and tunable open-system behavior on large-scale quantum hardware.
The intensely studied measurement-induced entanglement phase transition has become a hallmark of nonunitary quantum many-body dynamics. Usually, such a transition only appears at the level of each individual quantum trajectory, and is absent for the density matrix averaged over measurement outcomes. In this work, we introduce a class of adaptive random circuit models with feedback that exhibit transitions in both settings. After each measurement, a unitary operation is either applied or not depending on the measurement outcome, which steers the averaged density matrix towards a unique state above a certain measurement threshold. Interestingly, the transition for the density matrix and the entanglement transition in the individual quantum trajectory in general happen at different critical measurement rates. We demonstrate that the former transition belongs to the parity-conserving universality class by explicitly mapping to a classical branching-annihilating random-walk process.
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.
Stochastic resetting has emerged as a versatile protocol to drive quantum many-body systems to non-equilibrium steady states by interspersing unitary dynamics with measurements and resets at random times. In spite of this, a quantum hardware validation of such non-equilibrium steady states is still missing. Here, we achieve this goal by first formulating a noisy discrete-time theory where unitary gates alternate with noisy mid-circuit projective measurements and conditional resets. This noisy conditional resetting theory is then demonstrated on a superconducting quantum processor for up to N=7 qubits. We consider, as a paradigmatic case, the unitary dynamics of the interacting Floquet transverse-field Ising model. The stationary state of the noisy conditional resetting agrees quantitatively with the experiments, and it shows crossover behavior related to the equilibrium quantum phase transition of the model. Our results might thus pave the way for the preparation of collective stationary states on noisy quantum devices and for further developments of quantum algorithms involving mid-circuit measurements.
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.
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.