Simulations of quantum double models

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dc.creatorBrennen, G. K.
dc.creatorAguado, M.
dc.creatorCirac, J. I.
dc.date2009-01-10
dc.date.accessioned2026-07-07T13:17:25Z
dc.date.available2026-07-07T13:17:25Z
dc.descriptionWe demonstrate how to build a simulation of two dimensional physical theories describing topologically ordered systems whose excitations are in one to one correspondence with irreducible representations of a Hopf algebra, D(G), the quantum double of a finite group G. Our simulation uses a digital sequence of operations on a spin lattice to prepare a ground "vacuum" state and to create, braid and fuse anyonic excitations. The simulation works with or without the presence of a background Hamiltonian though only in the latter case is the system topologically protected. We describe a physical realization of a simulation of the simplest non-Abelian model, D(S_3), using trapped neutral atoms in a two dimensional optical lattice and provide a sequence of steps to perform universal quantum computation with anyons. The use of ancillary spin degrees of freedom figures prominently in our construction and provides a novel technique to prepare and probe these systems.
dc.description24 pages, 2 figures
dc.identifierhttps://arxiv.org/abs/0901.1345
dc.identifierhttp://arxiv.org/abs/0901.1345
dc.identifierNew J. Phys. 11 053009 (2009)
dc.identifierdoi:10.1088/1367-2630/11/5/053009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/231108
dc.subjectQuantum Physics
dc.subjectOther Condensed Matter
dc.titleSimulations of quantum double models
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