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

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dc.creatorGriffin, Tom
dc.creatorBartlett, Stephen D.
dc.date2008-05-19
dc.date2009-01-05
dc.date.accessioned2026-07-07T12:23:33Z
dc.date.available2026-07-07T12:23:33Z
dc.descriptionWe 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.
dc.description16 pages, 5 figures, comments welcome; v2 added some new results about exact solutions to this model; v3 published version
dc.identifierhttps://arxiv.org/abs/0805.2980
dc.identifierhttp://arxiv.org/abs/0805.2980
dc.identifierPhys. Rev. A 78, 062306 (2008)
dc.identifierdoi:10.1103/PhysRevA.78.062306
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/214029
dc.subjectQuantum Physics
dc.titleSpin lattices with two-body Hamiltonians for which the ground state encodes a cluster state
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