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arXiv · 1407.2777

Scheme for constructing graphs associated with stabilizer quantum codes

Carlo Cafaro·Damian Markham·Peter van Loock
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Abstract

We propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code; second, the canonical form of the CWS code is uncovered; third, the input vertices are attached to the graphs. To check the effectiveness of the scheme, we discuss several graphical constructions of various useful stabilizer codes characterized by single and multi-qubit encoding operators. In particular, the error-correcting capabilities of such quantum codes are verified in graph-theoretic terms as originally advocated by Schlingemann and Werner. Finally, possible generalizations of our scheme for the graphical construction of both (stabilizer and nonadditive) nonbinary and continuous-variable quantum codes are briefly addressed.

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Carlo Cafaro, Damian Markham, Peter van Loock. 2014-07-10. Scheme for constructing graphs associated with stabilizer quantum codes. https://arxiv.org/abs/1407.2777

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