Quantum error-correcting codes associated with graphs
<|reference_start|>Quantum error-correcting codes associated with graphs: 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.<|reference_end|>
@article{schlingemann2000quantum,
    title={Quantum error-correcting codes associated with graphs},
    author={D. Schlingemann and R.F. Werner},
    journal={arXiv preprint arXiv:quant-ph/0012111},
    year={2000},
    doi={10.1103/PhysRevA.65.012308},
    archivePrefix={arXiv},
    eprint={quant-ph/0012111},
    primaryClass={quant-ph cs.IT math-ph math.IT math.MP}
}