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A Performance Analysis of Quantum Low-Density Parity-Check Codes for Correcting Correlated Errors

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Abstract

In this paper we analyse the performance of quantum low-density parity-check (LDPC) codes over quantum memory channels for correcting correlated errors, where the quantum LDPC codes we use are the hypergraph product quantum LDPC codes. We generalize the classical Gilbert-Elliot markovian memory channel to the quantum Gilbert-Elliot channel and use it to model the memory effect in quantum memory channels. The simulation results show the memory effects in quantum GE channels has a bad effect to the performance of hypergraph product quantum LDPC codes. Then we propose a concatenation scheme by serially concatenating two hypergraph product quantum LDPC codes and it is shown that the serial concatenation scheme can improve the performance of hypergraph product quantum LDPC codes and lower down the error floor over quantum GE channels.

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Acknowledgment

The author is grateful to the Editor and the anonymous reviewers for their constructive comments and suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 61802175).

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Authors and Affiliations

  1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu Province, China

    Jihao Fan

  2. Key Laboratory of Computer Network and Information Integration of Ministry of Education, Southeast University, Nanjing, 211189, China

    Jihao Fan

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  1. Jihao Fan
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Correspondence to Jihao Fan.

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Fan, J. A Performance Analysis of Quantum Low-Density Parity-Check Codes for Correcting Correlated Errors. Int J Theor Phys 59, 3769–3777 (2020). https://doi.org/10.1007/s10773-020-04630-x

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