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Topological Quantum Error Correction with Optimal Encoding Rate

H. Bombin·M. A. Martin-Delgado
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Abstract

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.

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H. Bombin, M. A. Martin-Delgado. 2006-02-06. Topological Quantum Error Correction with Optimal Encoding Rate. https://doi.org/10.1103/physreva.73.062303

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