Topological order and criticality in (2+1)D monitored random quantum circuits

Abstract

It has recently been discovered that random quantum circuits provide an avenue to realize rich entanglement phase diagrams, which are hidden to standard expectation values of operators. Here we study (2+1)D random circuits with random Clifford unitary gates and measurements designed to stabilize trivial area law and topologically ordered phases. With competing single qubit Pauli-Z and toric code stabilizer measurements, in addition to random Clifford unitaries, we find a phase diagram involving a tricritical point that maps to (2+1)D percolation, a possibly stable critical phase, topologically ordered, trivial, and volume law phases, and lines of critical points separating them. With Pauli-Y single qubit measurements instead, we find an anisotropic self-dual tricritical point, with dynamical exponent $z\approx 1.46$, exhibiting logarithmic violation of the area law and an anomalous exponent for the topological entanglement entropy, which thus appears distinct from any known percolation fixed point. The phase diagram also hosts a measurement-induced volume law entangled phase in the absence of unitary dynamics.

published version

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Cited by in corpus (86)

• Random Quantum Circuits
• Growth of entanglement entropy under local projective measurements
• Fractal, logarithmic and volume-law entangled non-thermal steady states via spacetime duality
• Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions
• Theory of free fermions under random projective measurements
• Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements
• Measurement-induced phase transitions in $(d+1)$-dimensional stabilizer circuits
• Topological transitions with continuously monitored free fermions
• Dynamical purification and the emergence of quantum state designs from the projected ensemble
• Measurement-induced phase transition for free fermions above one dimension
• Floquet codes without parent subsystem codes
• Controlling entanglement at absorbing state phase transitions in random circuits
• Transitions in the learnability of global charges from local measurements
• Universality in driven open quantum matter
• Disordered monitored free fermions
• Measurement-induced criticality as a data-structure transition
• Full counting statistics as probe of measurement-induced transitions in the quantum Ising chain
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Measurement-induced purification in large-N hybrid Brownian circuits
• Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution
• Coherence requirements for quantum communication from hybrid circuit dynamics
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Diagnosing entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition
• Many-Body Non-Hermitian Skin Effect for Multipoles
• Non-Hermitian topology in monitored quantum circuits
• Measurement-induced transitions for interacting fermions
• Decodable hybrid dynamics of open quantum systems with Z_2 symmetry
• Infinite-randomness criticality in monitored quantum dynamics with static disorder
• Detecting and stabilizing measurement-induced symmetry-protected topological phases in generalized cluster models
• Percolation-induced PT symmetry breaking
• Surface codes, quantum circuits, and entanglement phases
• Evolution of many-body systems under ancilla quantum measurements
• Entanglement dynamics with string measurement operators
• Exponential shortcut to measurement-induced entanglement phase transitions
• Robust teleportation of a surface code and cascade of topological quantum phase transitions
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Boundary transfer matrix spectrum of measurement-induced transitions
• Three-fold way of entanglement dynamics in monitored quantum circuits
• Efficient sampling of noisy shallow circuits via monitored unraveling
• Entanglement Transitions in Unitary Circuit Games
• Localization, fractality, and ergodicity in a monitored qubit
• Entanglement and absorbing state transitions in $(d+1)$-dimensional stabilizer circuits
• Production of lattice gauge-Higgs topological states in measurement-only quantum circuit
• Quantum simulation using noisy unitary circuits and measurements
• Stable measurement-induced Floquet enriched topological order
• Magic transition in measurement-only circuits
• Structured volume-law entanglement in an interacting, monitored Majorana spin liquid
• Ancilla quantum measurements on interacting chains: Sensitivity of entanglement dynamics to the type and concentration of detectors
• Steering-induced phase transition in measurement-only quantum circuits
• Generalizing measurement-induced phase transitions to information exchange symmetry breaking
• Bulk-Measurement-Induced Boundary Phase Transition in Toric Code and Gauge-Higgs Model
• Gapless Symmetry-Protected Topological States in Measurement-Only Circuits
• Phase transition and evidence of fast-scrambling phase in measurement-only quantum circuit
• Entanglement transitions induced by quantum-data collection
• Entanglement dynamics in monitored Kitaev circuits: loop models, symmetry classification, and quantum Lifshitz scaling
• Interplay between lattice gauge theory and subsystem codes
• Topological Modes in Monitored Quantum Dynamics
• Controlling measurement-induced phase transitions with tunable detector coupling
• Topological physics in quantum critical systems
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Topology and Spectrum in Measurement-Induced Phase Transitions
• Measurement-induced phase transitions for free fermions in a quasiperiodic potential
• Measurement-only dynamical phase transition of topological and boundary order in toric code and gauge-Higgs models
• Multipartite entanglement structure of monitored quantum circuits
• Subsystem symmetry, spin glass order, and criticality from random measurements in a two-dimensional Bacon-Shor circuit
• Qubit Vitrification and Entanglement Criticality on a Quantum Simulator
• Kibble-Zurek mechanism and errors of gapped quantum phases
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Entanglement transitions in the quantum Ising chain: A comparison between different unravelings of the same Lindbladian
• Multipartite Greenberger-Horne-Zeilinger Entanglement in Monitored Random Clifford Circuits
• Quantum Entanglement Phase Transitions and Computational Complexity: Insights from Ising Models
• Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information
• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States
• The geometric phase transition of the three-dimensional ${\mathbb{Z}}_2$ lattice gauge model
• Quantum conditional mutual information as a probe of measurement-induced entanglement phase transitions
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• Measurement-induced criticality in extended and long-range unitary circuits
• Measurement-only circuit of perturbed toric code on triangular lattice: Topological entanglement, 1-form symmetry and logical qubits
• Disappearance of measurement-induced phase transition in a quantum spin system for large sizes
• Frustration-Free Control and Absorbing-State Transport in Entangled State Preparation
• Noisy Monitored Quantum Circuits
• Non-commutative Index of Measurement-only Entanglement Phase Transition
• Non-Commutative weak measurements: Entanglement, Symmetry Breaking, and the Role of Readout
• Generation of Volume-Law Entanglement by Local-Measurement-Only Quantum Dynamics