Toric codes and quantum doubles from two-body Hamiltonians

Details Toric codes and quantum doubles from two-body Hamiltonians Toric codes and quantum doubles from two-body Hamiltonians

2010-11-08

arxiv.org/abs/1011.1942v4

New J. Phys. 13, 053039 (2011)

Physics

Quantum Physics

10 pages of ideas plus 26 pages of calculations; 8 figures. v2, improved discussion of perturbation theory and relation to oth

Scientific paper

10.1088/1367-2630/13/5/053039

We present 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 PEPS description of the target models, and reproduces the target models' behavior using only couplings which are natural in terms of the original Hamiltonians. This allows our construction to exactly capture the symmetries of the target models.

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