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Quantum error-correcting codes associated with graphs

D. Schlingemann·R. F. Werner
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Abstract

We present a construction scheme 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 1-error correcting property of fivefold codes in any dimension. As new examples we construct a large class of codes saturating the singleton bound, as well as a tenfold code detecting 3 errors.

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D. Schlingemann, R. F. Werner. 2000-12-20. Quantum error-correcting codes associated with graphs. https://doi.org/10.1103/physreva.65.012308

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