# 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

# Topological quantum codes from self-complementary self-dual graphs

, Volume 14 (11) – Sep 3, 2015
10 pages

/lp/springer_journal/topological-quantum-codes-from-self-complementary-self-dual-graphs-0kkv2MBuLd
Publisher
Springer US
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-015-1115-9
Publisher site
See Article on Publisher Site

### 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 $$GF(p^{r})$$ 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.

### Journal

Quantum Information ProcessingSpringer Journals

Published: Sep 3, 2015

### References

• Binary construction of quantum codes of minimum distances five and six
Li, R; Li, X

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