Hybrid valence-bond states for universal quantum computation

Abstract

The spin-3/2 Affleck-Kennedy-Lieb-Tasaki (AKLT) valence-bond state on the hexagonal lattice was shown to be a universal resource state for measurement-based quantum computation (MBQC). Can AKLT states of higher spin magnitude support universal MBQC? We demonstrate that several hybrid 2D AKLT states involving mixture of spin-2 and other lower-spin entities, such as spin-3/2 and spin-1, are also universal for MBQC. This significantly expands universal resource states in the AKLT family. Even though frustration may be a hinderance to quantum computational universality, lattices can be modified to yield AKLT states that are universal. The family of AKLT states thus provides a versatile playground for quantum computation.

8 pages, 5 figures, title changed in published version

References in corpus (18)

• Resource-efficient linear optical quantum computation
• Valence Bond Solids for Quantum Computation
• Novel schemes for measurement-based quantum computation
• Universal resources for measurement-based quantum computation
• Measurement-based quantum computation beyond the one-way model
• Computational power of correlations
• 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
• Percolation, renormalization, and quantum computing with non-deterministic gates
• Quantum computational capability of a 2D valence bond solid phase
• Quantum computation by local measurement
• Phase transition of computational power in the resource states for one-way quantum computation
• Thermal States as Universal Resources for Quantum Computation with Always-on Interactions
• Spectral gaps of AKLT Hamiltonians using Tensor Network methods
• Quantum state reduction for universal measurement based computation
• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• Graph states as ground states of two-body frustration-free Hamiltonians
• Transitions in the quantum computational power

Cited by in corpus (27)

• Universal quantum computation using fractal symmetry-protected cluster phases
• Symmetry-protected topological phases with uniform computational power in one dimension
• Demonstrating the AKLT spectral gap on 2D degree-3 lattices
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• 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
• Quantum spin systems for measurement-based quantum computation
• Universal measurement-based quantum computation in two-dimensional SPT phases
• A class of two-dimensional AKLT models with a gap
• Quantum information in the Posner model of quantum cognition
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• AKLT models on decorated square lattices are gapped
• Quantum Algorithms for Inverse Participation Ratio Estimation in multi-qubit and multi-qudit systems
• Multi-qubit quantum computing using discrete-time quantum walks on closed graphs
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Random translation-invariant Hamiltonians and their spectral gaps
• The AKLT model on a hexagonal chain is gapped
• Response to defects in multi- and bipartite entanglement of isotropic quantum spin networks
• Negativity in the Generalized Valence Bond Solid State
• On the critical finite-size gap scaling for frustration-free Hamiltonians
• A Nonvanishing Spectral Gap for AKLT Models on Generalized Decorated Graphs
• The AKLT models on the singly decorated diamond lattice and two degree-4 planar lattices are gapped
• Haldane phases and phase diagrams of the S = 3/2, 1 bilinear-biquadratic Heisenberg model on the orthogonal dimer chain
• Kitaev Meets Affleck-Kennedy-Lieb-Tasaki: Competing Quantum Disorder in Spin-3/2 Honeycomb Systems