Today I read a paper titled “Topological Quantum Error Correction with Optimal Encoding Rate”
The abstract is:
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.