Identifying phases of quantum many-body systems that are universal for quantum computation

Abstract

Quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state, such as the ground state of an interacting many-body system. We investigate a simple spin-lattice system based on the cluster-state model, and by using nonlocal correlation functions that quantify the fidelity of quantum gates performed between distant qubits, we demonstrate that it possesses a quantum (zero-temperature) phase transition between a disordered phase and an ordered "cluster phase" in which it is possible to perform a universal set of quantum gates.

5 pages, 2 figures, comments welcome; v2 has had many technical detailed removed, and gives a simplified presentation; v3 published version

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Cited by in corpus (102)

• Subsystem symmetry protected topological order
• Graphical calculus for Gaussian pure states
• Symmetry-protected phases for measurement-based quantum computation
• Statistical mechanics of the Cluster-Ising model
• Quantum phase transition between cluster and antiferromagnetic states
• Identification of symmetry-protected topological states on noisy quantum computers
• A computationally universal phase of quantum matter
• Confined phases of one-dimensional spinless fermions coupled to $Z_2$ gauge theory
• Computational Power of Symmetry-Protected Topological Phases
• Verification of Many-Qubit States
• Spurious topological entanglement entropy from subsystem symmetries
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Topological order in 1D Cluster state protected by symmetry
• Universal quantum computation using fractal symmetry-protected cluster phases
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Symmetry protected topological order at nonzero temperature
• Phase diagram and quench dynamics of the Cluster-XY spin chain
• Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
• Verified measurement-based quantum computing with hypergraph states
• Quantum computational renormalization in the Haldane phase
• Mixed-state long-range order and criticality from measurement and feedback
• Symmetry protection of measurement-based quantum computation in ground states
• Gauging the Kitaev chain
• 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
• Symmetry-protected self-correcting quantum memories
• Emergent phase transition in Cluster Ising model with dissipation
• Quantum simulation of three-body interactions in weakly driven quantum systems
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Subsystem symmetry enriched topological order in three dimensions
• MERA for Spin Chains with Continuously Varying Criticality
• Qudit quantum computation on matrix product states with global symmetry
• Local characterization of 1d topologically ordered states
• Measurement-Based Quantum Computation
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Symmetry-Protected Topological Entanglement
• Kennedy-Tasaki transformation and non-invertible symmetry in lattice models beyond one dimension
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Transitions in the computational power of thermal states for measurement-based quantum computation
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c=m/2
• Zero modes of the Kitaev chain with phase-gradients and longer range couplings
• Stabilizer disentangling of conformal field theories
• Optical spin-1 chain and its use as a quantum computational wire
• Adiabatic Quantum Transistors
• Quenching Dynamics and Quantum Information
• Holonomic quantum computing in symmetry-protected ground states of spin chains
• Graph states as ground states of two-body frustration-free Hamiltonians
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• Generalized Graph States Based on Hadamard Matrices
• 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
• Arboreal Bound Entanglement
• Exact solution of a cluster model with next-nearest-neighbor interaction
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• Universal structure of measurement-induced information in many-body ground states
• Geometry of reduced density matrices for symmetry-protected topological phases
• 3-Fermion topological quantum computation
• Stable Symmetry-Protected Topological Phases in Systems with Heralded Noise
• Bounds on universal quantum computation with perturbed 2d cluster states
• Constructing Landau framework for topological order: Quantum chains and ladders
• String order via Floquet interactions in atomic systems
• Entanglement dynamics and phase transitions of the Floquet cluster spin chain
• Identification of topological phases using classically-optimized variational quantum eigensolver
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Characterization of variational quantum algorithms using free fermions
• Quantum circuits for spin and flavor degrees of freedom of quarks forming nucleons
• Quantum criticality in many-body parafermion chains
• Transitions in the quantum computational power
• Bifurcation in ground-state fidelity for a one-dimensional spin model with competing two-spin and three-spin interactions
• The Gauge Theory of Measurement-Based Quantum Computation
• Quantum computation by teleportation and symmetry
• Geometric Entanglement and Quantum Phase Transition in Generalized Cluster-XY models
• Clustering of conditional mutual information and quantum Markov structure at arbitrary temperatures
• Quantifying Entanglement in Cluster States Built with Error-Prone Interactions
• Variational Tensor Network Operator
• Quantum teleportation implies symmetry-protected topological order
• Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication
• Advancing Hybrid Quantum-Classical Algorithms via Mean-Operators
• Complete characterization of spin chains with two Ising symmetries
• Efficient entanglement length measurements for photonic cluster state sources
• Topological and Error-Correcting Properties for Symmetry-Protected Topological Order
• Simulating violation of causality using a topological phase transition
• Counter-intuitive yet efficient regimes for measurement based quantum computation on symmetry protected spin chains
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking
• Phase transitions in (2 + 1)D subsystem-symmetric monitored quantum circuits
• Computational Characterization of Symmetry-Protected Topological Phases in Open Quantum Systems
• Entanglement entropy of two disjoint intervals and spin structures in interacting chains in and out of equilibrium
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• A Subsystem Ginzburg-Landau and SPT Orders Co-existing on a Graph
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Sub-Riemannian geometry of measurement based quantum computation
• Robust Mixed-State Cluster States and Spurious Topological Entanglement Negativity
• Resource complexity of Symmetry Protected Topological phases
• Duality in spin systems via the $SU(4)$ algebra