The 2D AKLT state on the honeycomb lattice is a universal resource for quantum computation

Abstract

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state. Resource states can arise from ground states of carefully designed two-body interacting Hamiltonians. This opens up an appealing possibility of creating them by cooling. The family of Affleck-Kennedy-Lieb-Tasaki (AKLT) states are the ground states of particularly simple Hamiltonians with high symmetry, and their potential use in quantum computation gives rise to a new research direction. Expanding on our prior work [T.-C. Wei, I. Affleck, and R. Raussendorf, Phys. Rev. Lett. 106, 070501 (2011)], we give detailed analysis to explain why the spin-3/2 AKLT state on a two-dimensional honeycomb lattice is a universal resource for measurement-based quantum computation. Along the way, we also provide an alternative proof that the 1D spin-1 AKLT state can be used to simulate arbitrary one-qubit unitary gates. Moreover, we connect the quantum computational universality of 2D random graph states to their percolation property and show that these states whose graphs are in the supercritical (i.e. percolated) phase are also universal resources for measurement-based quantum computation.

21 pages, 13 figures, long version of Phys. Rev. Lett. 106, 070501 (2011) or arXiv:1102.5064

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• Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets
• 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
• Qudit quantum computation on matrix product states with global symmetry
• Universal measurement-based quantum computation with spin-2 Affleck-Kennedy-Lieb-Tasaki states
• Symmetry-protected topologically ordered states for universal quantum computation
• Measurement-Based Quantum Computation
• Measurement induced entanglement transition in two dimensional shallow circuit
• Hybrid valence-bond states for universal quantum computation
• Quantum spin systems for measurement-based quantum computation
• 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
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• Quantum computational universality of spin-3/2 Affleck-Kennedy-Lieb-Tasaki states beyond the honeycomb lattice
• Universal quantum computing using $({\mathbb{Z}}_d{)}^3$ symmetry-protected topologically ordered states
• Hubbard model for spin-1 Haldane chains
• Electrically driven singlet-triplet transition in triangulene spin-1 chains
• Emergence of the XY-like phase in the deformed spin-3/2 AKLT systems
• Symmetric Finite-Time Preparation of Cluster States via Quantum Pumps
• Efficient verification of Affleck-Kennedy-Lieb-Tasaki states
• Some aspects of Affleck-Kennedy-Lieb-Tasaki models: tensor network, physical properties, spectral gap, deformation, and quantum computation
• Efficient Verification of Ground States of Frustration-Free Hamiltonians
• Measurement-Based Quantum Computation on Two-Body Interacting Qubits with Adiabatic Evolution
• Quantitatively improved finite-size criteria for spectral gaps
• Spin-1 Haldane chains of superconductor-semiconductor hybrids
• Efficient detection of useful long-range entanglement in imperfect cluster states
• Building Symmetry Enriched Topological Phases from a Bipartite Lattice Construction and Anyon Condensation
• Preparing matrix product states via fusion: constraints and extensions
• Local dynamics and detection of topology in spin-1 chains
• Non-onsite symmetries and quantum teleportation in split-index matrix product states
• Deformations of the Boundary Theory of the Square Lattice AKLT Model
• Phases and phase transitions of an $S=3/2$ chain on metallic and semi-metallic surfaces