Topological Quantum Error Correction with Optimal Encoding Rate

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.Comment: REVTEX4 file, 5 figure