2000/12/20 by D. Schlingemann, R. F. Werner · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #quant-ph #cs.IT #math-ph #math.IT #math.MP
paper · pdf · doi:10.1103/physreva.65.012308
8 pages revtex, 5 figures
arxiv created 2000/12/20 · arxiv updated 2013/05/29
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.