Topological quantum error correction with optimal encoding rate
Héctor Bombín, Miguel Angel Martin-Delgado · Physical Review A · 2006
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.