Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Lindblad non-universality of measurement phases and phase transitions

Michael Kolodrubetz

Published Nov 22, 2021• 0 citations
OpenAlex

Abstract

Entanglement phase transitions in hybrid quantum circuits are generally argued to be properties of the individual trajectories rather than measurement-averaged dynamics, despite the fact that results of measurements are not used for feedback in the steady state. Here, we explicitly demonstrate this difference by constructing a family of hybrid quantum circuits with identical measurement-averaged dynamics that give different phases and phase transitions. We propose measurement-averaged destruction of Bell state entanglement as a proxy for determining which hybrid circuit yields the lowest-entanglement dynamics and show that it holds numerically for the measurements we consider. We comment on implications for quantum computing and noisy quantum circuits.

Related papers

Optimality of Lindblad unfolding in measurement phase transitions

Michael Kolodrubetz

Entanglement phase transitions in hybrid quantum circuits describe individual quantum trajectories rather than the measurement-averaged ensemble, despite the fact that results of measurements are not conventionally used for feedback. Here, we numerically demonstrate that a class of generalized measurements with identical measurement-averaged dynamics give different phases and phase transitions. We show that measurement-averaged destruction of Bell state entanglement is a useful proxy for determining which hybrid circuit yields the lowest-entanglement dynamics. We use this to argue that no unfolding of our model can avoid a volume law phase, which has implications for simulation of open quantum systems.

arXiv:2111.11391•Physical review. B./Physical review. B•Apr 13, 2023•9 citations

Measurement-and Feedback-Driven Non-Equilibrium Phase Transitions on a Quantum Processor

Zhiyi Wu, Xuandong Sun, Songlei Wang +8 more

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.

quant-pharXiv:2512.07966•Physical Review Letters•Dec 10, 2025•0 citations

Entanglement steering in adaptive circuits with feedback

Vikram Ravindranath, Yiqiu Han, Zhi-Cheng Yang +1 more

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.

arXiv:2211.05162•Physical review. B./Physical review. B•Jul 12, 2023•48 citations

Measurement-induced purification in large- N hybrid Brownian circuits

Gregory S. Bentsen, Subhayan Sahu, Brian G. Swingle

Competition between unitary dynamics that scrambles quantum information nonlocally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. Here we study this phenomenon in an analytically tractable all-to-all Brownian hybrid circuit model composed of qubits. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or totally destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables which are distinguished by the averaging procedure, and for concreteness we focus on a particular purity quantity for which the averaging is particularly simple. We represent the purity as a path integral coupling four replicas with twisted boundary conditions. Saddle-point analysis reveals a second-order phase transition corresponding to replica permutation symmetry breaking below a critical measurement rate. The transition is mean-field-like and we characterize the critical properties near the transition in terms of a simple Ising field theory in $0+1$ dimensions. In addition to studying the purity of the entire system, we study subsystem purities and relate these results to manifestations of quantum error correction in the model. We also comment on the experimental feasibility for simulating this averaged purity, and corroborate our results with exact diagonalization for modest system sizes.

arXiv:2104.07688•Physical review. B./Physical review. B•Sep 7, 2021•49 citations

Simulering av mätningsinducerade övergångar i sammanflätningsentropi

Evelina Stenseth

Measurement-induced entanglement transitions arise in quantum circuits of unitary gates and measurements, referred to as hybrid circuits. On average, unitary dynamics generate entanglement, and measurements suppress entanglement. In one-dimensional hybrid circuits, this competition leads to a transition between an area-law phase when the probability of measurements is higher, and a volume-law entangled phase when the probability is lower. In this thesis, the phase transition is studied using two different approaches. First, state vector simulations are performed for hybrid circuits composed of Haar-random unitary gates and random Clifford gates. This allows for direct access to the state vectors and entanglement entropy, but is only feasible for smaller size systems (up to 12 qubits). Second, a traffic flow model is implemented as an approximation to stabiliser dynamics of Clifford circuits, which is studied for larger systems (up to 2048 qubits). Scaling analyses are carried out for both approaches to investigate the dependence of the steady-state entropy on system size and measurement probability. Data collapses of simulation data for different circuit sizes are obtained using both a logarithmic form S−αlnN and by also including an additional correction S−αlnN+βN^(−ω) where ω = 1, leading to a more accurate collapse for smaller sizes. Both the state vector model and traffic flow model lead to a phase transition in entanglement entropy, but with different critical parameters. This indicates that the traffic flow model and the quantum circuit models do not belong to the same universality class. The results clarify the efficiency but also limitations of classical models for describing measurement-induced entanglement transitions.

•Jan 1, 2026•0 citations

Quantum Zeno effect and the many-body entanglement transition

Yaodong Li, Xiao Chen, Matthew P. A. Fisher

We introduce and explore a one-dimensional ``hybrid'' quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a ``quantum Zeno phase'' where strong measurements suppress the entanglement growth to saturate in an area law. Extensive numerical simulations of the quantum trajectories of the many-particle wave functions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable ``weak measurement phase'' that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a continuous quantum dynamical phase transition between the ``weak measurement phase'' and the ``quantum Zeno phase,'' driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady-state and dynamic critical properties of this quantum entanglement transition are accessed.

arXiv:1808.06134•Physical review. B./Physical review. B•Nov 19, 2018•709 citations
Entanglement phase transitions in hybrid quantum circuits are generally argued to be properties of the individual trajectories rather than measurement-averaged dynamics, despite the fact that results of measurements are not used for feedback in the steady state. Here, we explicitly demonstrate this difference by constructing a family of hybrid quantum circuits with identical measurement-averaged dynamics that give different phases and phase transitions. We propose measurement-averaged destruction of Bell state entanglement as a proxy for determining which hybrid circuit yields the lowest-entanglement dynamics and show that it holds numerically for the measurements we consider. We comment on implications for quantum computing and noisy quantum circuits.
Entanglement phase transitions in hybrid quantum circuits describe individual quantum trajectories rather than the measurement-averaged ensemble, despite the fact that results of measurements are not conventionally used for feedback. Here, we numerically demonstrate that a class of generalized measurements with identical measurement-averaged dynamics give different phases and phase transitions. We show that measurement-averaged destruction of Bell state entanglement is a useful proxy for determining which hybrid circuit yields the lowest-entanglement dynamics. We use this to argue that no unfolding of our model can avoid a volume law phase, which has implications for simulation of open quantum systems.
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.
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.
Competition between unitary dynamics that scrambles quantum information nonlocally and local measurements that probe and collapse the quantum state can result in a measurement-induced entanglement phase transition. Here we study this phenomenon in an analytically tractable all-to-all Brownian hybrid circuit model composed of qubits. The system is initially entangled with an equal sized reference, and the subsequent hybrid system dynamics either partially preserves or totally destroys this entanglement depending on the measurement rate. Our approach can access a variety of entropic observables which are distinguished by the averaging procedure, and for concreteness we focus on a particular purity quantity for which the averaging is particularly simple. We represent the purity as a path integral coupling four replicas with twisted boundary conditions. Saddle-point analysis reveals a second-order phase transition corresponding to replica permutation symmetry breaking below a critical measurement rate. The transition is mean-field-like and we characterize the critical properties near the transition in terms of a simple Ising field theory in 0+10+10+1 dimensions. In addition to studying the purity of the entire system, we study subsystem purities and relate these results to manifestations of quantum error correction in the model. We also comment on the experimental feasibility for simulating this averaged purity, and corroborate our results with exact diagonalization for modest system sizes.
Measurement-induced entanglement transitions arise in quantum circuits of unitary gates and measurements, referred to as hybrid circuits. On average, unitary dynamics generate entanglement, and measurements suppress entanglement. In one-dimensional hybrid circuits, this competition leads to a transition between an area-law phase when the probability of measurements is higher, and a volume-law entangled phase when the probability is lower. In this thesis, the phase transition is studied using two different approaches. First, state vector simulations are performed for hybrid circuits composed of Haar-random unitary gates and random Clifford gates. This allows for direct access to the state vectors and entanglement entropy, but is only feasible for smaller size systems (up to 12 qubits). Second, a traffic flow model is implemented as an approximation to stabiliser dynamics of Clifford circuits, which is studied for larger systems (up to 2048 qubits). Scaling analyses are carried out for both approaches to investigate the dependence of the steady-state entropy on system size and measurement probability. Data collapses of simulation data for different circuit sizes are obtained using both a logarithmic form S−αlnN and by also including an additional correction S−αlnN+βN^(−ω) where ω = 1, leading to a more accurate collapse for smaller sizes. Both the state vector model and traffic flow model lead to a phase transition in entanglement entropy, but with different critical parameters. This indicates that the traffic flow model and the quantum circuit models do not belong to the same universality class. The results clarify the efficiency but also limitations of classical models for describing measurement-induced entanglement transitions.
We introduce and explore a one-dimensional ``hybrid'' quantum circuit model consisting of both unitary gates and projective measurements. While the unitary gates are drawn from a random distribution and act uniformly in the circuit, the measurements are made at random positions and times throughout the system. By varying the measurement rate we can tune between the volume law entangled phase for the random unitary circuit model (no measurements) and a ``quantum Zeno phase'' where strong measurements suppress the entanglement growth to saturate in an area law. Extensive numerical simulations of the quantum trajectories of the many-particle wave functions (exploiting Clifford circuitry to access systems up to 512 qubits) provide evidence for a stable ``weak measurement phase'' that exhibits volume-law entanglement entropy, with a coefficient decreasing with increasing measurement rate. We also present evidence for a continuous quantum dynamical phase transition between the ``weak measurement phase'' and the ``quantum Zeno phase,'' driven by a competition between the entangling tendencies of unitary evolution and the disentangling tendencies of projective measurements. Detailed steady-state and dynamic critical properties of this quantum entanglement transition are accessed.