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Some quantum synchronizable codes with explicit distance

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Abstract

Quantum synchronizable codes can be used to guard against both the interference of quantum noise on qubits and misalignment in block synchronization. In this paper, we utilize classical BCH codes to obtain three classes of quantum synchronizable codes. These codes can achieve the best achievable synchronization recovery capabilities. By computing the exact minimum distance of classical BCH codes, we determine the error-correcting performance towards Pauli errors of the resulting synchronizable codes.

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Acknowledgements

The authors would like to thank the anonymous referees who gave many helpful comments and suggestions to greatly improve the presentation of the paper. This work is supported by the National Natural Science Foundation of China under Grant Nos. 61972126, 62002093, U21A20428 and 12171134.

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Authors and Affiliations

  1. School of Mathematics, Hefei University of Technology, Hefei, 230601, China

    Taoran Liu & Xiaoshan Kai

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  1. Taoran Liu
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Correspondence to Xiaoshan Kai.

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Liu, T., Kai, X. Some quantum synchronizable codes with explicit distance. J. Appl. Math. Comput. 69, 1751–1764 (2023). https://doi.org/10.1007/s12190-022-01811-1

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  • DOI: https://doi.org/10.1007/s12190-022-01811-1

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