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Scheme for constructing graphs associated with stabilizer quantum codes

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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https://hal.telecom-paris.fr/hal-02287093
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Submitted on : Friday, September 13, 2019 - 4:34:47 PM
Last modification on : Tuesday, October 19, 2021 - 11:15:19 AM

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  • HAL Id : hal-02287093, version 1

Citation

Carlo Cafaro, Damian Markham, Peter van Loock. Scheme for constructing graphs associated with stabilizer quantum codes. Physical Review A, American Physical Society 2015. ⟨hal-02287093⟩

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