A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound

Daniel Gottesman

doi:10.1103/PhysRevA.54.1862

A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound

Quantum Physics 2009-10-30 v2

Authors: Daniel Gottesman

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Abstract

I develop methods for analyzing quantum error-correcting codes, and use these methods to construct an infinite class of codes saturating the quantum Hamming bound. These codes encode $k=n-j-2$ qubits in $n=2^j$ qubits and correct $t=1$ error.

Keywords

quantum error correction

Cite

@article{arxiv.quant-ph/9604038,
  title  = {A Class of Quantum Error-Correcting Codes Saturating the Quantum Hamming Bound},
  author = {Daniel Gottesman},
  journal= {arXiv preprint arXiv:quant-ph/9604038},
  year   = {2009}
}

Comments

REVTeX, 22 pages; introduction clarified and corrected to explicitly include non-orthogonal codes, claim of appendix A restricted to possibly allow some 1-error degenerate codes, references added; to appear in Phys. Rev. A

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