Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields

Abstract

We consider a one-dimensional spin chain for which the ground state is the cluster state, capable of functioning as a quantum computational wire when subjected to local adaptive measurements of individual qubits, and investigate the robustness of this property to local and coupled (Ising-type) perturbations. We investigate the ground state both by identifying suitable correlation functions as order parameters, as well as numerically using a variational method based on matrix product states. We find that the model retains an infinite localizable entanglement length for Ising and local fields up to a quantum phase transition, but that the resulting entangled state is not simply characterized by a Pauli correction based on the measurement results.

11 pages, 7 figures, comments welcome; v2 gives some further analytic results for the localizable entanglement, and some additional references; v3 published version

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Cited by in corpus (62)

• Statistical mechanics of the Cluster-Ising model
• Quantum phase transition between cluster and antiferromagnetic states
• Topological order in 1D Cluster state protected by symmetry
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Experimental quantum state measurement with classical shadows
• Phase diagram and quench dynamics of the Cluster-XY spin chain
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Quantum computational renormalization in the Haldane phase
• Measurement-based quantum computation in a 2D phase of matter
• Fate of the cluster state on the square lattice in a magnetic field
• Realizing all $so(N{)}_1$ quantum criticalities in symmetry protected cluster models
• Emergent phase transition in Cluster Ising model with dissipation
• Post measurement bipartite entanglement entropy in conformal field theories
• Entanglement entropy after a partial projective measurement in $1+1$ dimensional conformal field theories: exact results
• Quantum Sampling Algorithms for Near-Term Devices
• Local characterization of 1d topologically ordered states
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Symmetry-Protected Topological Entanglement
• Topological and dynamical properties of a generalized cluster model in one dimension
• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• Stabilizer disentangling of conformal field theories
• Scaling of geometric phase versus band structure in cluster-Ising models
• Quenching Dynamics and Quantum Information
• Entanglement dynamics of one-dimensional driven spin systems in time-varying magnetic fields
• Estimating localizable entanglement from witnesses
• Holonomic quantum computing in symmetry-protected ground states of spin chains
• Scalable characterization of localizable entanglement in noisy topological quantum codes
• Entanglement entropy after selective measurements in quantum chains
• Generalized Graph States Based on Hadamard Matrices
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Quantum computation via measurements on the low-temperature state of a many-body system
• Topological pumping of quantum correlations
• Edge modes and symmetry-protected topological states in open quantum systems
• Quantum Sampling Algorithms, Phase Transitions, and Computational Complexity
• Exact solution of a cluster model with next-nearest-neighbor interaction
• Geometry of reduced density matrices for symmetry-protected topological phases
• Tensor networks demonstrate the robustness of localization and symmetry protected topological phases
• String order via Floquet interactions in atomic systems
• Quantum reservoir probing of quantum phase transitions
• Entanglement dynamics and phase transitions of the Floquet cluster spin chain
• Matrix Product States with long-range Localizable Entanglement
• Phase diagram and sweep dynamics of a one-dimensional generalized cluster model
• Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions
• Genuine Multipartite Entanglement induced by a Thermal Acoustic Reservoir
• Controlling gain with loss: Bounds on localizable entanglement in multi-qubit systems
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Distinguishing Phases via Non-Markovian Dynamics of Entanglement in Topological Quantum Codes under Parallel Magnetic Field
• Quantum teleportation implies symmetry-protected topological order
• Localizing genuine multiparty entanglement in noisy stabilizer states
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• The global phase diagram of the cluster-XY spin chain with dissipation
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Efficient entanglement length measurements for photonic cluster state sources
• Topological and Error-Correcting Properties for Symmetry-Protected Topological Order
• Non-onsite symmetry breaking: topological phase coexistence and criticality
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• One-dimensional $Z_2$ lattice gauge theory in periodic Gauss-law sectors
• Quantum correlations in a cluster spin model with three-spin interactions
• Recovery of resources through sequential noisy measurements
• Logarithmic growth of peripheral entanglement concentrated via noisy measurements in a star network of spins
• Entanglement transition in a cluster spin chain coupled with free spins
• Unfolding the Toric Code Model with Emergent Qubits