Efficient Mitigation of Error Floors in Quantum Error Correction using Non-Binary Low-Density Parity-Check Codes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909595312586752 |
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| author | Kasai, Kenta |
| author_facet | Kasai, Kenta |
| contents | In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated noise becomes trapped, and develop tailored decoding methods for each cycle type. For Type-I cycles, we propose a method to make the difference between estimated and true noise degenerate. Type-II cycles are shown to be uncorrectable, while for Type-III cycles, we utilize the fact that cycles in non-binary LDPC codes do not necessarily correspond to codewords, allowing us to estimate the true noise. Our method significantly improves decoding performance and reduces error floors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13923 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Efficient Mitigation of Error Floors in Quantum Error Correction using Non-Binary Low-Density Parity-Check Codes Kasai, Kenta Quantum Physics Information Theory In this paper, we propose an efficient method to reduce error floors in quantum error correction using non-binary low-density parity-check (LDPC) codes. We identify and classify cycle structures in the parity-check matrix where estimated noise becomes trapped, and develop tailored decoding methods for each cycle type. For Type-I cycles, we propose a method to make the difference between estimated and true noise degenerate. Type-II cycles are shown to be uncorrectable, while for Type-III cycles, we utilize the fact that cycles in non-binary LDPC codes do not necessarily correspond to codewords, allowing us to estimate the true noise. Our method significantly improves decoding performance and reduces error floors. |
| title | Efficient Mitigation of Error Floors in Quantum Error Correction using Non-Binary Low-Density Parity-Check Codes |
| topic | Quantum Physics Information Theory |
| url | https://arxiv.org/abs/2501.13923 |