Quantum spin systems for measurement-based quantum computation

Abstract

Measurement-based quantum computation is different from other approaches for quantum computation, in that everything needs to be done is only local measurement on a certain entangled state. It thus uses entanglement as the resource that drives computation. We give a pedagogical treatment on the basics, and then review some selected developments beyond graph states, including Affleck-Kennedy-Lieb-Tasaki states and more recent 2D symmetry-protected topological states.

arXiv comment18 pages, 13 figures, review article in 2018

References in corpus (89)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Surface codes: Towards practical large-scale quantum computation
• Experimental realisation of the topological Haldane model
• Persistent entanglement in arrays of interacting particles
• Quantum Teleportation is a Universal Computational Primitive
• A quantum gas microscope - detecting single atoms in a Hubbard regime optical lattice
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Experimental One-Way Quantum Computing
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• Measurement-based quantum computation
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Quantum Simulation of Antiferromagnetic Spin Chains in an Optical Lattice
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• A Rydberg Quantum Simulator
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Fault-tolerant quantum computation with high threshold in two dimensions
• Resource-efficient linear optical quantum computation
• Classifying quantum phases using Matrix Product States and PEPS
• Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms
• Experimental entanglement of six photons in graph states
• Topological fault-tolerance in cluster state quantum computation
• Optical quantum computation using cluster states
• Braiding statistics approach to symmetry-protected topological phases
• Ultra-Large-Scale Continuous-Variable Cluster States Multiplexed in the Time Domain
• Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb
• Experimental Demonstration of Blind Quantum Computing
• Universal blind quantum computation
• Controlled exchange interaction between pairs of neutral atoms in an optical lattice
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Complete classification of 1D gapped quantum phases in interacting spin systems
• Deterministic Generation of a Cluster State of Entangled Photons
• A fault-tolerant one-way quantum computer
• Cluster-state quantum computation
• A photonic cluster state machine gun
• Valence Bond Solids for Quantum Computation
• One-Way Quantum Computing in the Optical Frequency Comb
• Most quantum states are too entangled to be useful as computational resources
• Novel schemes for measurement-based quantum computation
• Measurement-based quantum computation beyond the one-way model
• Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing
• Quantum simulation of 2d topological physics using orbital-angular-momentum-carrying photons in a 1d array of cavities
• Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Symmetry-protected phases for measurement-based quantum computation
• Optically generated 2-dimensional photonic cluster state from coupled quantum dots
• Unified derivations of measurement-based schemes for quantum computation
• Creation, manipulation, and detection of Abelian and non-Abelian anyons in optical lattices
• Are random pure states useful for quantum computation?
• Measurement-based quantum computation with trapped ions
• Quantum computational capability of a 2D valence bond solid phase
• Ultracompact Generation of Continuous-Variable Cluster States
• Excitations and the tangent space of projected entangled-pair states
• Classical simulation versus universality in measurement based quantum computation
• Fundamentals of universality in one-way quantum computation
• Computational Power of Symmetry-Protected Topological Phases
• Optical one-way quantum computing with a simulated valence-bond solid
• Gapped Two-body Hamiltonian whose Unique Ground State is Universal for One-way Quantum Computation
• A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
• On measurement-based quantum computation with the toric code states
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Gapped boundaries, group cohomology and fault-tolerant logical gates
• Quantum computation by local measurement
• Symmetry-protected topological phases with uniform computational power in one dimension
• The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation
• Measurement-based quantum computation in a 2D phase of matter
• Phase transition of computational power in the resource states for one-way quantum computation
• Graph states as ground states of many-body spin-1/2 Hamiltonians
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Symmetry-protected topologically ordered states for universal quantum computation
• Quantum state reduction for universal measurement based computation
• Hybrid valence-bond states for universal quantum computation
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Order and Disorder in AKLT Antiferromagnets in Three Dimensions
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• Quantum states far from the energy eigenstates of any local Hamiltonian
• Two-dimensional Valence Bond Solid (AKLT) states from $t_{2g}$ electrons
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• AKLT Models with Quantum Spin Glass Ground States
• Measurement-Based Quantum Computing with Valence-Bond-Solids
• Complete Characterization of the Ground Space Structure of Two-Body Frustration-Free Hamiltonians for Qubits
• Graph states as ground states of two-body frustration-free Hamiltonians
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Linear-optical simulation of the cooling of a cluster-state Hamiltonian system
• Quantum computational tensor network on string-net condensate
• Spectral properties for a family of two-dimensional quantum antiferromagnets

Cited by in corpus (19)

• Many-body quantum magic
• Universal quantum computation using fractal symmetry-protected cluster phases
• Universal measurement-based quantum computation in a one-dimensional architecture enabled by dual-unitary circuits
• Generation of Photonic Matrix Product States with Rydberg Atomic Arrays
• AKLT models on decorated square lattices are gapped
• Strong-to-weak symmetry breaking states in stochastic dephasing stabilizer circuits
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Measurement-based quantum simulation of Abelian lattice gauge theories
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata
• Broadcasting single-qubit and multi-qubit-entangled states: authentication, cryptography, and distributed quantum computation
• Anomaly inflow, dualities, and quantum simulation of abelian lattice gauge theories induced by measurements
• Quantum simulation of lattice gauge theories via deterministic duality transformations assisted by measurements
• Quantum computation by teleportation and symmetry
• Anomaly inflow for CSS and fractonic lattice models and dualities via cluster state measurement
• Bulk and boundary entanglement transitions in the projective gauge-Higgs model
• Quantum teleportation implies symmetry-protected topological order
• Preparing matrix product states via fusion: constraints and extensions
• Hierarchy of emergent cluster states by measurement from symmetry-protected-topological states with large symmetry to subsystem cat state
• Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit