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Non-binary quantum synchronizable codes based on cyclic codes over \(\textrm{F}_q\)

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Abstract

Quantum synchronizable codes (QSCs) are special quantum error-correcting codes which can be used to correct the effects of quantum noise on qubits and misalignment in block synchronization. In this paper, we first construct a new class of QSCs from cyclic codes of length \(2^n\), by using the cyclotomic cosets. Besides, we give another new class of QSCs based on BCH codes of length an integer N satisfying some certain conditions. The synchronization capabilities of all these QSCs are always the upper bound. In addition, the lower bounds of correcting bit errors and phase errors for these codes are also given.

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Acknowledgements

The authors would like to express the great appreciation to the patient reviewer especially for his/her constructive comments which greatly improved the innovation and readability of this paper. Besides, the authors are also thankful to the Shandong Provincial Natural Science Foundation, China (No. ZR2022MA061) and National Natural Science Foundation of China (No. 61902429) and the Graduate Innovation Project of China University of Petroleum (East China) (No. YCX2021137) and the Fundamental Research Funds for the Central Universities (No. 22CX03015A).

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Authors and Affiliations

  1. College of Sciences, China University of Petroleum (East China), Huangdao, Qingdao, 266580, Shandong, China

    Shiwen Sun, Tongjiang Yan, Yuhua Sun, Tao Wang & Xueting Wang

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  1. Shiwen Sun
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  3. Yuhua Sun
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Contributions

Tongjiang Yan is assigned as Corresponding Author and acts on behalf of all co-authors and ensures that questions related to the accuracy or integrity of any part of the work are appropriately addressed. Shiwen Sun contributed to the study conception and design. The first draft of the manuscript was written by Shiwen Sun, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Tongjiang Yan.

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Sun, S., Yan, T., Sun, Y. et al. Non-binary quantum synchronizable codes based on cyclic codes over \(\textrm{F}_q\). Quantum Inf Process 22, 72 (2023). https://doi.org/10.1007/s11128-022-03794-1

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