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The application of weight parity error correction in quantum codes

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Abstract

Weight parity error correction (WPEC) is an error-correction scheme that can correct high-weight Pauli errors. Still, it was initially shown to apply only to Steane and Golay codes. In this work, we prove that the WPEC scheme is appropriate for concatenated codes constructed from two classes of quantum codes, quantum quadratic-residue codes and quantum stabilizer codes from self-orthogonal cyclic codes. We generalize the implementation of the WPEC technique to nonbinary quantum codes and provide an application using WPEC for the \([[121, 1, 25]]_3\) concatenated code. We also show that the WPEC may not be applicable for some quantum codes with specific parameters through an example of the [[15, 7]] code over \({{\mathbb {F}}}_2\).

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Acknowledgements

The authors are grateful to the anonymous referees for careful reading and for many valuable suggestions.

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Authors and Affiliations

  1. The State Key Laboratory of Mathematical Engineering and Advanced Computing, Zhengzhou, 450001, China

    Chao Du, Yiting Liu & Zhi Ma

  2. Henan Key Laboratory of Network Cryptography Technology, Zhengzhou, 450001, Henan, China

    Chao Du, Yiting Liu & Zhi Ma

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  1. Chao Du
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  2. Yiting Liu
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  3. Zhi Ma
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Correspondence to Zhi Ma.

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This work was supported by the National Key R &D Program of China (No. 2021YFB3100100) and the National Natural Science Foundation of China (Grants Nos. 61972413,61901525,62002385).

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Du, C., Liu, Y. & Ma, Z. The application of weight parity error correction in quantum codes. Quantum Inf Process 22, 50 (2023). https://doi.org/10.1007/s11128-022-03790-5

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