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Quantum stabilizer codes constructed from sparse matrices have good performance and can be efficiently decoded by belief propagation (BP).
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M. R. Yazdani, S. Hemati, and A. H. Banihashemi, “Improving belief propagation on graphs with cycles,” IEEE Commun. Lett. , vol. 8, pp. 57–59, 2004
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A. Rigby, J. C. Olivier, and P. Jarvis, “Modified belief propagation decoders for quantum low-density parity-check codes,” Phys. Rev. A , vol. 100, p. 012330, 2019
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Y.-H. Liu and D. Poulin, “Neural belief-propagation decoders for quantum error-correcting codes,” Phys. Rev. Lett. , vol. 122, p. 200501, 2019
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K.-Y. Kuo and C.-Y. Lai, “The encoding and decoding complexities of entanglement-assisted quantum stabilizer codes,” in Proc. IEEE Int. Symp. Inf. Theory , 2019, pp. 2893–2897
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K.-Y. Kuo and C.-C. Lu, “On the hardnesses of several quantum decoding problems,” Quant. Inf. Process. , vol. 19, pp. 1–17, 2020
2020
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