Critical properties of the measurement-induced transition in random quantum circuits

  title={Critical properties of the measurement-induced transition in random quantum circuits},
  author={Aidan Zabalo and Michael J. Gullans and Justin H. Wilson and Sarang Gopalakrishnan and David A. Huse and Jedediah H. Pixley},
  journal={Physical Review B},
We numerically study the measurement-driven quantum phase transition of Haar-random quantum circuits in $1+1$ dimensions. By analyzing the tripartite mutual information we are able to make a precise estimate of the critical measurement rate $p_c = 0.17(1)$. We extract estimates for the associated bulk critical exponents that are consistent with the values for percolation, as well as those for stabilizer circuits, but differ from previous estimates for the Haar-random case. Our estimates of the… 

Figures and Tables from this paper

Measurement-induced criticality in (2+1) -dimensional hybrid quantum circuits
We investigate the dynamics of two-dimensional quantum spin systems under the combined effect of random unitary gates and local projective measurements. When considering steady states, a
Measurement-induced criticality and entanglement clusters: A study of one-dimensional and two-dimensional Clifford circuits
Entanglement transitions in quantum dynamics present a novel class of phase transitions in nonequilibrium systems. When a many-body quantum system undergoes unitary evolution interspersed with
Measurement-induced quantum criticality under continuous monitoring
We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory
Probing sign structure using measurement-induced entanglement
The sign structure of quantum states is closely connected to quantum phases of matter, yet detecting such fine-grained properties of amplitudes is subtle. Here we employ as a diagnostic
Measurement-induced topological entanglement transitions in symmetric random quantum circuits
Random quantum circuits, in which an array of qubits is subjected to a series of randomly chosen unitary operations, have provided key insights into the dynamics of many-body quantum entanglement.
Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory
This work introduces theoretical approaches to measurement-induced phase transitions (MPT) and also to entanglement transitions in random tensor networks, and proposes Landau-Ginsburg-Wilson-like field theories for the MPT, the FMPT, and for entanglements in Tensor networks.
Measurement-induced criticality in extended and long-range unitary circuits
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
Quantum Coding with Low-Depth Random Circuits
It is found that for any rate beneath the capacity, high-performing codes with thousands of logical qubits are achievable with depth 4-8 expurgated random circuits in $D=2$ dimensions.
Topological order and entanglement dynamics in the measurement-only XZZX quantum code
We examine the dynamics of a (1 + 1) -dimensional measurement-only circuit defined by the stabilizers of the [[5,1,3]] quantum error correcting code interrupted by single-qubit Pauli measurements. The
Dynamical Purification Phase Transition Induced by Quantum Measurements
Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We


Measurement-induced criticality in random quantum circuits
We investigate the critical behavior of the entanglement transition induced by projective measurements in (Haar) random unitary quantum circuits. Using a replica approach, we map the calculation of
Measurement-Induced Phase Transitions in the Dynamics of Entanglement
We define dynamical universality classes for many-body systems whose unitary evolution is punctuated by projective measurements. In cases where such measurements occur randomly at a finite rate $p$
Quantum Entanglement Growth Under Random Unitary Dynamics
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of
Quantum Zeno effect and the many-body entanglement transition
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
Entanglement transition from variable-strength weak measurements
We show that weak measurements can induce a quantum phase transition of interacting many-body systems from an ergodic thermal phase with a large entropy to a nonergodic localized phase with a small
Measurement-driven entanglement transition in hybrid quantum circuits
Quantum information tends to spread out in interacting systems, leading to thermalization as characterized by the volume-law entropy of entanglement, while local measurements that extract classical
Solution of a Minimal Model for Many-Body Quantum Chaos
We solve a minimal model for quantum chaos in a spatially extended many-body system. It consists of a chain of sites with nearest-neighbour coupling under Floquet time evolution. Quantum states at
Linking numbers for self-avoiding loops and percolation: application to the spin quantum hall transition
  • Cardy
  • Physics
    Physical review letters
  • 2000
As an application, the exact value sqrt[3]/2 is computed for the conductivity at the spin Hall transition, as well as the shape dependence of the mean conductance in an arbitrary simply connected geometry with two extended edge contacts.
Evolution of Entanglement Spectra under Generic Quantum Dynamics.
It is found that the entanglement spectrum of a subsystem evolves with three distinct timescales, and features hold for chaotic Hamiltonian and Floquet dynamics as well as a range of quantum circuit models.
Improved Simulation of Stabilizer Circuits
The Gottesman-Knill theorem, which says that a stabilizer circuit, a quantum circuit consisting solely of controlled-NOT, Hadamard, and phase gates can be simulated efficiently on a classical computer, is improved in several directions.