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(pr), where p is a prime number and r is a positive integer. The parameters of two new classes of quantum codes are [[(2k+2)(8k+ 7); 2(8k^2+7k); d]] and [[(2k+2)(8k+9); 2(8k^2+9k+1); d]] respectively, where d>=3. For these quantum codes, the code rate approaches 1 as k goes to infinity.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(pr), where p is a prime number and r is a positive integer. The parameters of two new classes of quantum codes are [[(2k+2)(8k+ 7); 2(8k^2+7k); d]] and [[(2k+2)(8k+9); 2(8k^2+9k+1); d]] respectively, where d>=3. For these quantum codes, the code rate approaches 1 as k goes to infinity.

arXiv:1503.05710Mar 19, 20150 citations

Topological Quantum Codes

Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares

SpringerBriefs in mathematicsJan 1, 20220 citations

New classes of TQC associated with self-dual, quasi self-dual and denser tessellations

Clarice Dias de Albuquerque, Reginaldo Palazzo, Eduardo Brandani da Silva

In this paper we present six classes of topological quantum codes (TQC) on compact surfaces with genus $g\ge 2$ . These codes are derived from self-dual, quasi self-dual and denser tessellations associated with embeddings of self-dual complete graphs and complete bipartite graphs on the corresponding compact surfaces. The majority of the new classes has the self-dual tessellations as their algebraic and geometric supporting mathematical structures. Every code achieves minimum distance 3 and its encoding rate is such that $\frac{k}{n} \rightarrow 1$ as $n \rightarrow \infty$ , except for the one case where $\frac{k}{n} \rightarrow \frac{1}{3}$ as $n \rightarrow \infty$ .In this paper we present six classes of topological quantum codes (TQC) on compact surfaces with genus $g\ge 2$. These codes are derived from self-dual, quasi self-dual and denser tessellations associated with embeddings of self-dual complete graphs and complete bipartite graphs on the corresponding compact surfaces. The majority of the new classes has the self-dual tessellations as their algebraic and geometric supporting mathematical structures. Every code achieves minimum distance 3 and its encoding rate is such that $\frac{k}{n} \rightarrow 1$ as $n \rightarrow \infty$, except for the one case where $\frac{k}{n} \rightarrow \frac{1}{3}$ as $n \rightarrow \infty$.

Quantum Information and ComputationNov 1, 20109 citations

Quantum Codes for Topological Quantum Computation

Clarice Dias de Albuquerque, Eduardo Brandani da Silva, Waldir Silva Soares

SpringerBriefs in mathematicsJan 1, 20223 citations

Quantum Computation with Topological Codes

Keisuke Fujii

SpringerBriefs in mathematical physicsJan 1, 201559 citations

In this paper we present six classes of topological quantum codes (TQC) on compact surfaces with genus

g\ge 2

. These codes are derived from self-dual, quasi self-dual and denser tessellations associated with embeddings of self-dual complete graphs and complete bipartite graphs on the corresponding compact surfaces. The majority of the new classes has the self-dual tessellations as their algebraic and geometric supporting mathematical structures. Every code achieves minimum distance 3 and its encoding rate is such that

\frac{k}{n} \rightarrow 1

n \rightarrow \infty

, except for the one case where

\frac{k}{n} \rightarrow \frac{1}{3}

n \rightarrow \infty