Spin lattices with two-body Hamiltonians for which the ground state encodes a cluster state

Abstract

We present a general procedure for constructing lattices of qubits with a Hamiltonian composed of nearest-neighbour two-body interactions such that the ground state encodes a cluster state. We give specific details for lattices in one-, two-, and three-dimensions, investigating both periodic and fixed boundary conditions, as well as present a proof for the applicability of this procedure to any graph. We determine the energy gap of these systems, which is shown to be independent of the size of the lattice but dependent on the type of lattice (in particular, the coordination number), and investigate the scaling of this gap in terms of the coupling constants of the Hamiltonian. We provide a comparative analysis of the different lattice types with respect to their usefulness for measurement-based quantum computation.

16 pages, 5 figures, comments welcome; v2 added some new results about exact solutions to this model; v3 published version

References in corpus (16)

• Measurement-based quantum computation with cluster states
• Experimental One-Way Quantum Computing
• Resource-efficient linear optical quantum computation
• Topological fault-tolerance in cluster state quantum computation
• A fault-tolerant one-way quantum computer
• 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
• Measurement-based quantum computer in the gapped ground state of a two-body Hamiltonian
• Quantum Information Processing in Optical Lattices and Magnetic Microtraps
• Fundamentals of universality in one-way quantum computation
• A simple nearest-neighbor two-body Hamiltonian system for which the ground state is a universal resource for quantum computation
• The computational difficulty of finding MPS ground states
• Graph states as ground states of many-body spin-1/2 Hamiltonians
• Quantum states far from the energy eigenstates of any local Hamiltonian

Cited by in corpus (15)

• Identifying phases of quantum many-body systems that are universal for quantum computation
• Quantum computational capability of a 2D valence bond solid phase
• Verification of Many-Qubit States
• Phase transitions and localizable entanglement in cluster-state spin chains with Ising couplings and local fields
• Verified measurement-based quantum computing with hypergraph states
• Measurement-based quantum computation in a 2D phase of matter
• Generalized Cluster States Based on Finite Groups
• Optical spin-1 chain and its use as a quantum computational wire
• Graph states as ground states of two-body frustration-free Hamiltonians
• Quantum computation via measurements on the low-temperature state of a many-body system
• Entanglement in pure and thermal cluster states
• Bounds on universal quantum computation with perturbed 2d cluster states
• Measurement-Based Quantum Computation on Two-Body Interacting Qubits with Adiabatic Evolution
• Quantum phase transitions in the $K$-layer Ising toric code
• Spectral properties for a family of two-dimensional quantum antiferromagnets