Please use this identifier to cite or link to this item: https://doi.org/10.1088/1367-2630/13/6/065010
Title: Generating topological order from a two-dimensional cluster state using a duality mapping
Authors: Brown, B.J.
Son, W. 
Kraus, C.V.
Fazio, R.
Vedral, V. 
Issue Date: Jun-2011
Citation: Brown, B.J., Son, W., Kraus, C.V., Fazio, R., Vedral, V. (2011-06). Generating topological order from a two-dimensional cluster state using a duality mapping. New Journal of Physics 13 : -. ScholarBank@NUS Repository. https://doi.org/10.1088/1367-2630/13/6/065010
Abstract: In this paper, we prove, extend and review possible mappings between the two-dimensional (2D) cluster state, Wen's model, the 2D Ising chain and Kitaev's toric code model. We introduce a 2D duality transformation to map the 2D lattice cluster state into the topologically ordered Wen model. Then, we investigate how this mapping could be achieved physically, which allows us to discuss the rate at which a topologically ordered system can be achieved. Next, using a lattice fermionization method, Wen's model is mapped into a series of 1D Ising interactions. Considering the boundary terms with this mapping then reveals how the Ising chains interact with one another. The duality of these models can be taken as a starting point to address questions as to how their gate operations in different quantum computational models can be related to each other. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Source Title: New Journal of Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/117026
ISSN: 13672630
DOI: 10.1088/1367-2630/13/6/065010
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