Graphical Nonbinary Quantum Error-Correcting Codes

Abstract

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.

12 pages, 5 figures (pdf)

References in corpus (5)

• Multi-party entanglement in graph states
• Topological Quantum Distillation
• Experimental entanglement of six photons in graph states
• Correcting Quantum Errors with Entanglement
• A simple family of nonadditive quantum codes

Cited by in corpus (9)

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• Greenberger-Horne-Zeilinger paradoxes from qudit graph states
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• Parafermion stabilizer codes
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• Decoder for Nonbinary CWS Quantum Codes
• A new approach to codeword stabilized quantum codes using the algebraic structure of modules
• Separable Operations, Graph Codes and the Location of Quantum Information
• New quantum MDS codes derived from constacyclic codes