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Toric codes and quantum doubles from two-body Hamiltonians

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Published 20 May 2011 Published under licence by IOP Publishing Ltd
, , Citation Courtney G Brell et al 2011 New J. Phys. 13 053039 DOI 10.1088/1367-2630/13/5/053039

1367-2630/13/5/053039

Abstract

We present here a procedure to obtain the Hamiltonians of the toric code and Kitaev quantum double models as the low-energy limits of entirely two-body Hamiltonians. Our construction makes use of a new type of perturbation gadget based on error-detecting subsystem codes. The procedure is motivated by a projected entangled pair states (PEPS) description of the target models, and reproduces the target models' behavior using only couplings that are natural in terms of the original Hamiltonians. This allows our construction to capture the symmetries of the target models.

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10.1088/1367-2630/13/5/053039