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Quantum Error Correction Fault Tolerance Open Quantum Systems Decoherence Quantum Simulation

Toric codes and quantum doubles from two-body Hamiltonians

arXiv

Authors: Courtney G. Brell, Steven T. Flammia, Stephen D. Bartlett, Andrew C. Doherty

Year

2010

Paper ID

10521

Status

Preprint

Abstract Read

~2 min

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Abstract

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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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.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1011.1942 [2] arXiv https://arxiv.org/abs/1011.1942 [3] Publisher https://arxiv.org/abs/1011.1942

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