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Quantum Error Correction Fault Tolerance

Graphical Quantum Error-Correcting Codes

arXiv
Authors: Sixia Yu, Qing Chen, C. H. Oh

Year

2007

Paper ID

49101

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes. Almost all quantum codes constructed so far are stabilizer (additive) codes and the construction of nonadditive codes, which are potentially more efficient, is not as well understood as that of stabilizer codes. Our graphical approach provides a unified and classical way to construct both stabilizer and nonadditive codes. In particular we have explicitly constructed the optimal ((10,24,3)) code and a family of 1-error detecting nonadditive codes with the highest encoding rate so far. In the case of stabilizer codes a thorough search becomes tangible and we have classified all the extremal stabilizer codes up to 8 qubits.

Why This Paper Matters

  • This paper contributes to the Quantum Error Correction & Fault Tolerance research area in the Quantum Articles archive.
  • It adds a 2007 reference point for readers tracking recent quantum research.
  • We introduce a purely graph-theoretical object, namely the coding clique, to construct quantum errorcorrecting codes.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:0709.1780 [2] arXiv https://arxiv.org/abs/0709.1780 [3] Publisher https://arxiv.org/abs/0709.1780

Local Citation Graph (Related-Paper Links)

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