Nishimori's cat: stable long-range entanglement from finite-depth unitaries and weak measurements

Abstract

In the field of monitored quantum circuits, it has remained an open question whether finite-time protocols for preparing long-range entangled states lead to phases of matter which are stable to gate imperfections, which can convert projective into weak measurements. Here we show that in certain cases, long-range entanglement persists in the presence of weak measurements, and gives rise to novel forms of quantum criticality. We demonstrate this explicitly for preparing the two-dimensional Greenberger-Horne-Zeilinger cat state and the three-dimensional toric code as minimal instances. In contrast to the monitored random unitary circuits, In contrast to random monitored circuits, our circuit of gates and measurements is deterministic; the only randomness is in the measurement outcomes. We show how the randomness in these weak measurements allows us to track the solvable Nishimori line of the random-bond Ising model, rigorously establishing the stability of the glassy long-range entangled states in two and three spatial dimensions. Away from this exactly solvable construction, we use hybrid tensor network and Monte Carlo simulations to obtain a nonzero Edwards-Anderson order parameter as an indicator of long-range entanglement in the two-dimensional scenario. We argue that our protocol admits a natural implementation in existing quantum computing architectures, requiring only a depth-3 circuit on IBM's heavy-hexagon transmon chips.

arXiv comment4.5 + 10 pages, 2 + 8 figures

References in corpus (82)

• Fault-tolerant quantum computation by anyons
• Introduction to Quantum Noise, Measurement and Amplification
• Persistent entanglement in arrays of interacting particles
• Topological quantum memory
• Encoding a qubit in an oscillator
• Many-Body Physics with Individually-Controlled Rydberg Atoms
• Quantum Phases of Matter on a 256-Atom Programmable Quantum Simulator
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Quantum Computational Supremacy
• Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
• Measurement-Induced Phase Transitions in the Dynamics of Entanglement
• Quantum Zeno Effect and the Many-body Entanglement Transition
• Area laws in quantum systems: mutual information and correlations
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Criticality, the area law, and the computational power of PEPS
• Quantum Simulators: Architectures and Opportunities
• Theory of the phase transition in random unitary circuits with measurements
• Measurement-induced criticality in random quantum circuits
• Random Quantum Circuits
• Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition
• A fault-tolerant one-way quantum computer
• Dynamical purification phase transitions induced by quantum measurements
• Topological Order and Conformal Quantum Critical Points
• Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory
• Measurement-Induced Entanglement Transitions in the Quantum Ising Chain: From Infinite to Zero Clicks
• Entanglement transition from variable-strength weak measurements
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Measurement-induced topological entanglement transitions in symmetric random quantum circuits
• Measurement Protected Quantum Phases
• Measurement-induced quantum criticality under continuous monitoring
• Long-range quantum entanglement in noisy cluster states
• Quantum Sampling Problems, BosonSampling and Quantum Supremacy
• Challenges and Opportunities of Near-Term Quantum Computing Systems
• Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
• Entanglement renormalization and topological order
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Topological order in a 3D toric code at finite temperature
• SYK meets non-Hermiticity II: measurement-induced phase transition
• Efficient classical simulation of random shallow 2D quantum circuits
• Quantum phase transitions in matrix product systems
• Solving the sampling problem of the Sycamore quantum circuits
• The two-dimensional random-bond Ising model, free fermions and the network model
• Verifying Multipartite Entangled GHZ States via Multiple Quantum Coherences
• Isometric Tensor Network States in Two Dimensions
• Universality of entanglement transitions from stroboscopic to continuous measurements
• Measurement as a shortcut to long-range entangled quantum matter
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Crossing a topological phase transition with a quantum computer
• Quantum Circuits assisted by LOCC: Transformations and Phases of Matter
• Many-Body Quantum Zeno Effect and Measurement-Induced Subradiance Transition
• Topological order and criticality in (2+1)D monitored random quantum circuits
• From classical to quantum dynamics at Rokhsar-Kivelson points
• A dual-element, two-dimensional atom array with continuous-mode operation
• Foliated Quantum Codes
• Nishimori point in the 2D +/- J random-bond Ising model
• Random-bond Ising model in two dimensions, the Nishimori line, and supersymmetry
• String and Membrane condensation on 3D lattices
• Criticality in the two-dimensional random-bond Ising model
• Topological transitions with continuously monitored free fermions
• Exact entanglement renormalization for string-net models
• Generation and verification of 27-qubit Greenberger-Horne-Zeilinger states in a superconducting quantum computer
• Absence of a metallic phase in random-bond Ising models in two dimensions: applications to disordered superconductors and paired quantum Hall states
• Phase Structure of the Random-Plaquette Z_2 Gauge Model: Accuracy Threshold for a Toric Quantum Memory
• Simulations of quantum double models
• Transitions in the learnability of global charges from local measurements
• Methods for simulating string-net states and anyons on a digital quantum computer
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• High Temperature Expansion Study of the Nishimori multicritical Point in Two and Four Dimensions
• Isometric Tensor Network representation of string-net liquids
• Topology, criticality, and dynamically generated qubits in a stochastic measurement-only Kitaev model
• Pivot Hamiltonians as generators of symmetry and entanglement
• Sequential generation of projected entangled-pair states
• Domain-Wall Energies and Magnetization of the Two-Dimensional Random-Bond Ising Model
• Phase transition of computational power in the resource states for one-way quantum computation
• Topological order and entanglement dynamics in the measurement-only XZZX quantum code
• Neural-Network Decoders for Measurement Induced Phase Transitions
• Skeleton of Matrix-Product-State-Solvable Models Connecting Topological Phases of Matter
• Measurement induced entanglement transition in two dimensional shallow circuit
• Tensor network approach to phase transitions of a non-Abelian topological phase
• Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
• Effect of quantum error correction on detection-induced coherent errors

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