Topological quantum codes from self-complementary self-dual graphs

Topological quantum codes from self-complementary self-dual graphs 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 $$GF(p^{r})$$ G F ( p r ) ”, where $$p\in {\mathbb {P}}$$ p ∈ P and $$r\in {\mathbb {Z}}^{+}$$ r ∈ Z + . The parameters of two new classes of quantum codes are $$[[(2k'+2)(8k'+7),2(8k'^{2}+7k'),d_\mathrm{min}]]$$ [ [ ( 2 k ′ + 2 ) ( 8 k ′ + 7 ) , 2 ( 8 k ′ 2 + 7 k ′ ) , d min ] ] and $$[[(2k'+2)(8k'+9),2(8k'^{2}+9k'+1),d_\mathrm{min}]]$$ [ [ ( 2 k ′ + 2 ) ( 8 k ′ + 9 ) , 2 ( 8 k ′ 2 + 9 k ′ + 1 ) , d min ] ] , respectively, where $$d_\mathrm{min}\ge 3$$ d min ≥ 3 . For these quantum codes, the code rate approaches 1 as $$k'$$ k ′ tends to infinity. Quantum Information Processing Springer Journals

Topological quantum codes from self-complementary self-dual graphs

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Springer US
Copyright © 2015 by Springer Science+Business Media New York
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
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