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Erschienen in:
01.11.2015
Topological quantum codes from self-complementary self-dual graphs
Erschienen in: Quantum Information Processing | Ausgabe 11/2015
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Abstract
In this paper, we present two new classes of binary quantum codes with minimum distance of at least three, by self-complementary self-dual orientable embeddings of “voltage graphs” and “Paley graphs in the Galois field \(GF(p^{r})\)”, where \(p\in {\mathbb {P}}\) and \(r\in {\mathbb {Z}}^{+}\). The parameters of two new classes of quantum codes are \([[(2k'+2)(8k'+7),2(8k'^{2}+7k'),d_\mathrm{min}]]\) and \([[(2k'+2)(8k'+9),2(8k'^{2}+9k'+1),d_\mathrm{min}]]\), respectively, where \(d_\mathrm{min}\ge 3\). For these quantum codes, the code rate approaches 1 as \(k'\) tends to infinity.