Quantum error-correcting codes associated with graphs

We present a construction for quantum error correcting codes. The basic ingredients are a graph and a finite Abelian group, from which the code can explicitly be obtained. We prove necessary and sufficient conditions for the graph such that the resulting code corrects a certain number of errors. This allows a simple verification of the one-error correcting property of codes of length 5 in any dimension. As examples, we construct a large class of maximum distance separable codes, i.e. codes saturating the Singleton bound, as well as a code of length 10 detecting three errors.

• Publication year

  2000

• Venue

  arXiv.org

• Publication date

  2000-12-20

• Fields of study

  Mathematics, Physics, Computer Science

• Identifiers
  DOI 10.1103/PhysRevA.65.012308arXiv quant-ph/0012111
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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