Topological Quantum Error Correction with Optimal Encoding Rate
Quantum Physics
2016-09-08 v2 Strongly Correlated Electrons
Graphics
High Energy Physics - Theory
Mathematical Physics
Algebraic Topology
Combinatorics
math.MP
Abstract
We prove the existence of topological quantum error correcting codes with encoding rates 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.
Cite
@article{arxiv.quant-ph/0602063,
title = {Topological Quantum Error Correction with Optimal Encoding Rate},
author = {H. Bombin and M. A. Martin-Delgado},
journal= {arXiv preprint arXiv:quant-ph/0602063},
year = {2016}
}
Comments
REVTEX4 file, 5 figures