Graphical Nonbinary Quantum Error-Correcting Codes

Details Graphical Nonbinary Quantum Error-Correcting Codes Graphical Nonbinary Quantum Error-Correcting Codes

2008-01-06

arxiv.org/abs/0801.0831v1

Physics

Quantum Physics

12 pages, 5 figures (pdf)

Scientific paper

10.1103/PhysRevA.78.012306

In this paper, based on the nonbinary graph state, we present a systematic way of constructing good non-binary quantum codes, both additive and nonadditive, for systems with integer dimensions. With the help of computer search, which results in many interesting codes including some nonadditive codes meeting the Singleton bounds, we are able to construct explicitly four families of optimal codes, namely, $[[6,2,3]]_p$, $[[7,3,3]]_p$, $[[8,2,4]]_p$ and $[[8,4,3]]_p$ for any odd dimension $p$ and a family of nonadditive code $((5,p,3))_p$ for arbitrary $p>3$. In the case of composite numbers as dimensions, we also construct a family of stabilizer codes $((6,2\cdot p^2,3))_{2p}$ for odd $p$, whose coding subspace is {\em not} of a dimension that is a power of the dimension of the physical subsystem.

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