Topological Quantum Error Correction with Optimal Encoding Rate
<|reference_start|>Topological Quantum Error Correction with Optimal Encoding Rate: 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.<|reference_end|>
@article{bombin2006topological,
    title={Topological Quantum Error Correction with Optimal Encoding Rate},
    author={H. Bombin, M.A. Martin-Delgado},
    journal={Phys.Rev.A73:062303,2006},
    year={2006},
    doi={10.1103/PhysRevA.73.062303},
    archivePrefix={arXiv},
    eprint={quant-ph/0602063},
    primaryClass={quant-ph cond-mat.str-el cs.GR hep-th math-ph math.AT math.CO math.MP}
}