Quantum Zeno effect and the many-body entanglement transition

By Yaodong Li, Xiao Chen, Matthew P. A. Fisher. Physical review B, 2018

511 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/4415b6c90a9ea5ec65fecfb08c2eb53c15dc7d11

Citations in the corpus

• Random Quantum Circuits (2022, unknown): “Numerical evidence for this transition has by now been found in a wide range of microscopic models (52, 53, 58, 68, 65, 66, 61, 62, 54, 63, 64, 77, 67).”
• Dynamical Purification Phase Transition Induced by Quantum Measurements (2019, unknown): “In the models considered below, based on random unitary circuits interspersed with projective measurements [25–27], capacity achieving states are (to our knowledge) unknown.”
• Statistical mechanics of quantum error correcting codes (2020, unknown): “5 In the case of a pure initial state [13, 15] where this transition was first found, p < pc corresponds to a “volume law entangled phase”, where one should be thinking in terms of the reduced (mixed) density matrix of a subsystem which holds a finite entropy density as T →∞.”
• Measurement-induced entanglement phase transition on a superconducting quantum processor with mid-circuit readout (2022, unknown): “The specific form of the ansatz remains a topic of discussion and depends on the structure of the random circuits [14, 16, 18, 44].”
• Measurement-induced quantum phases realized in a trapped-ion quantum computer (2021, unknown): “5, 1) and L = (4, 6, 8), and observe the first experimental evidence of the phases of a dynamical purification phase transition.”
• Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory (2020, unknown): “In the many-body case this random dynamics admits a “measurement phase transition” (MPT) between two qualitatively different, stable dynamical phases, with distinct entanglement properties [6–27].”
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect (2022, unknown): “Additionally, the measurement-induced phase transitions typically rely on spatial or temporal randomness and many-body interactions aside from some exceptions [14, 25].”
• Entanglement Membrane in Chaotic Many-Body Systems (2019, unknown): “[84] Yaodong Li, Xiao Chen, and Matthew PA Fisher.”