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Topological Quantum Error Correction with Optimal Encoding Rate

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arxiv quant-ph/0602063 v2 pith:TETACHQO submitted 2006-02-06 quant-ph cond-mat.str-elcs.GRhep-thmath-phmath.ATmath.COmath.MP

H. Bombin , M.A. Martin-Delgado This is my paper · ORCID
classification quant-phcond-mat.str-elcs.GRhep-thmath-phmath.ATmath.COmath.MP
keywords codestopologicalencodingerroroptimalquantumapproachingarbitrary
verification ladder T0 review T1 audit T2 compute T3 formal

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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.

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  1. A small and interesting architecture for early fault-tolerant quantum computers

    quant-ph 2025-07 conditional novelty 5.0 of 10

    An early fault-tolerant quantum computer architecture that uses teleportation between the [[4,2,2]] and [[8,3,2]] color codes for a universal transversal gate set, plus a mirror-circuit benchmarking protocol.

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