Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource

Abstract

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. The family of Affleck-Kennedy-Lieb-Tasaki states has recently been intensively explored and shown to provide restricted computation. Here, we show that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state on a honeycomb lattice is a universal resource for measurement-based quantum computation.

4+2 pages, 4 figures, PRL short version of arXiv:1009.2840, see also alternative approach by A. Miyake, arXiv:1009.3491

References in corpus (11)

• Multi-party entanglement in graph states
• Valence Bond Solids for Quantum Computation
• Novel schemes for measurement-based quantum computation
• Universal resources for measurement-based quantum computation
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Quantum computation on the edge of a symmetry-protected topological order
• Optical one-way quantum computing with a simulated valence-bond solid
• Phase transition of computational power in the resource states for one-way quantum computation
• Quantum computation in correlation space and extremal entanglement
• Quantum state reduction for universal measurement based computation
• Entanglement in valence-bond-solid states on symmetric graphs

Cited by in corpus (124)

• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Blind quantum computation protocol in which Alice only makes measurements
• Symmetry-protected phases for measurement-based quantum computation
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Quantum computational capability of a 2D valence bond solid phase
• Hierarchy of universal entanglement in 2D measurement-based quantum computation
• Verification of Many-Qubit States
• Ancilla-Driven Universal Blind Quantum Computation
• Quantum paramagnetic ground states on the honeycomb lattice and field-induced transition to Néel order
• Quantum paramagnets on the honeycomb lattice and field-induced Néel order: Possible application to Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$)
• Universal quantum computation using fractal symmetry-protected cluster phases
• Deterministic constant-depth preparation of the AKLT state on a quantum processor using fusion measurements
• Resource quality of a symmetry-protected topologically ordered phase for quantum computation
• Demon-like Algorithmic Quantum Cooling and its Realization with Quantum Optics
• Phase diagram and quench dynamics of the Cluster-XY spin chain
• Numerical treatment of spin systems with unrestricted spin length $S$: A functional renormalization group study
• Verified measurement-based quantum computing with hypergraph states
• Quantum computation by local measurement
• Symmetry-protected topological phases with uniform computational power in one dimension
• Symmetry protection of measurement-based quantum computation in ground states
• Negativity for two blocks in the one dimensional Spin 1 AKLT model
• Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets
• Entanglement Spectra of the 2D AKLT Model: VBS/CFT Correspondence
• Thermal States as Universal Resources for Quantum Computation with Always-on Interactions
• Proposal for Quantum Simulation via All-Optically Generated Tensor Network States
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• High-fidelity realization of the AKLT state on a NISQ-era quantum processor
• Existence of a Spectral Gap in the Affleck-Kennedy-Lieb-Tasaki Model on the Hexagonal Lattice
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Qudit quantum computation on matrix product states with global symmetry
• Symmetry-protected topologically ordered states for universal quantum computation
• Measurement-Based Quantum Computation
• Latent Computational Complexity of Symmetry-Protected Topological Order with Fractional Symmetry
• Measurement-driven navigation in many-body Hilbert space: Active-decision steering
• Theory of triangulene two-dimensional crystals
• Quantum spin systems for measurement-based quantum computation
• Hybrid valence-bond states for universal quantum computation
• Topologically protected measurement-based quantum computation on the thermal state of a nearest-neighbor two-body Hamiltonian with spin-3/2 particles
• The Existence of Featureless Paramagnets on the Square and the Honeycomb Lattices in 2+1D
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• Qudits for decomposing multiqubit gates and realizing quantum algorithms
• Universal measurement-based quantum computation in two-dimensional SPT phases
• Ground states of 1D symmetry-protected topological phases and their utility as resource states for quantum computation
• Preparing Valence-Bond-Solid states on noisy intermediate-scale quantum computers
• A class of two-dimensional AKLT models with a gap
• Measurement-Based Quantum Computation on Symmetry Breaking Thermal States
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Two-dimensional Valence Bond Solid (AKLT) states from $t_{2g}$ electrons
• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• Fermionic Measurement-based Quantum Computation
• AKLT models on decorated square lattices are gapped
• Symmetry Protected Quantum State Renormalization
• Measurement-Based Quantum Computing with Valence-Bond-Solids
• Broken-symmetry magnetic phases in two-dimensional triangulene crystals
• Hubbard model for spin-1 Haldane chains
• Acausal measurement-based quantum computing
• Structural, thermodynamic, and local probe investigations of a honeycomb material Ag${}_3$LiMn${}_2$O${}_6$
• Investigating global and topological order of states by local measurement and classical communication: Study on SPT phase diagrams by quantum energy teleportation
• An architecture for two-qubit encoding in neutral ytterbium-171 atoms
• Graph states as ground states of two-body frustration-free Hamiltonians
• Layer by layer generation of cluster states
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Topological qubits from valence bond solids
• Field-induced superfluids and Bose liquids in Projected Entangled Pair States
• Bounds on universal quantum computation with perturbed 2d cluster states
• Exact dimer phase with anisotropic interaction for one dimensional magnets
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Linear-optical simulation of the cooling of a cluster-state Hamiltonian system
• Quantum algorithm for preparing the ground state of a system via resonance transition
• Sequential measurement-based quantum computing with memories
• Measurement-Based Quantum Computation on Two-Body Interacting Qubits with Adiabatic Evolution
• Universal resources for quantum computing
• Quantum computational universality of the Cai-Miyake-Dür-Briegel 2D quantum state from Affleck-Kennedy-Lieb-Tasaki quasichains
• Random translation-invariant Hamiltonians and their spectral gaps
• Transitions in the quantum computational power
• AKLT-states as ZX-diagrams: diagrammatic reasoning for quantum states
• Entanglement of disjoint blocks in the one dimensional Spin 1 VBS
• Preserving universal resources for one-way quantum computing
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• The Gauge Theory of Measurement-Based Quantum Computation
• Compact quantum circuits from one-way quantum computation
• Qudit Shadow Estimation Based on the Clifford Group and the Power of a Single Magic Gate
• Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks
• Symmetry constraints on temporal order in measurement-based quantum computation
• MoP${}_3$SiO${}_{11}$: a $4d^3$ honeycomb antiferromagnet with disconnected octahedra
• Classification of measurement-based quantum wire in stabilizer PEPS
• The AKLT model on a hexagonal chain is gapped
• Quantum computation by teleportation and symmetry
• Phase transitions of a 2D deformed-AKLT model
• Negativity in the Generalized Valence Bond Solid State
• Quantum phases of spin-1 system on 3/4 and 3/5 skewed ladders
• Spectral properties for a family of two-dimensional quantum antiferromagnets
• Finding resource states of measurement-based quantum computing is harder than quantum computing
• Dimer states of Rydberg atoms on the Kagome lattice as resources for universal measurement-based quantum computation
• Perturbative 2-body Parent Hamiltonians for Projected Entangled Pair States
• Quantum phases of a frustrated spin-1 system: The 5/7 skewed ladder
• Catalytic Transformation from Computationally Universal to Strictly Universal Measurement-Based Quantum Computation
• Maximally entangled gapped ground state of lattice fermions
• Variational Quantum Simulation of Valence-Bond Solids
• A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs
• Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Topos logic in measurement-based quantum computation
• The AKLT models on the singly decorated diamond lattice and two degree-4 planar lattices are gapped
• Scheme for measurement-based quantum computation on projected entangled-pair states
• Designing a polymerized phenalenyl tessellation molecule to realize a super-honeycomb antiferromagnetic S = 3/2 spin system
• Hidden quantum correlations in the ground states of quasiclassical spin systems
• Sequential Generation of Two-dimensional Super-area-law States with Local Parent Hamiltonian
• Resource-efficient entanglement detection in high-dimensional states via two-qubit witnesses
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems
• Relative resilience to noise of standard and sequential approaches to measurement-based quantum computation
• Blindly Verifying Unknown Entanglement without State Tomography
• Measurement-based quantum computation cannot avoid byproducts
• Phases and phase transitions of an $S=3/2$ chain on metallic and semi-metallic surfaces
• Measurement-Based Quantum Computation Using the Spin-1 XXZ Model with Uniaxial Anisotropy
• Generalization of the Affleck-Kennedy-Lieb-Tasaki Model for Quantum Ferromagnetism
• Extension of the Lieb-Schupp theorem to the Heisenberg models with higher order interactions