Topological Quantum Error Correction with Optimal Encoding Rate

02/06/2006

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by   H. Bombin, et al.

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We prove the existence of topological quantum error correcting codes with encoding rates k/n asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of arbitrary genus. We find a class of regular toric codes that are optimal. For physical implementations, we present planar topological codes.