Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/87906
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- Title
- Simulations of quantum double models
- Related
- New journal of physics, Vol. 11, May 2009, p.1-33
- DOI
- 10.1088/1367-2630/11/5/053009
- Publisher
- IOP Publishing
- Date
- 2009
- Author/Creator
- Brennen, G. K
- Author/Creator
- Aguado, M
- Author/Creator
- Cirac, J. I
- Description
- We demonstrate how to build a simulation of two-dimensional (2D) 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 in a spin lattice model originally due to Kitaev 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(S₃), using trapped neutral atoms in a 2D 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.
- Description
- 33 page(s)
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Physics and Engineering
- Identifier
- http://hdl.handle.net/1959.14/87906
- Identifier
- ISSN:1367-2630
- Identifier
- mq-rm-2009005365
- Language
- eng
- Rights
- Copyright 2009 IOP Publishing and Deutsche Physikalische Gesellschaft. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.
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