Bidirectional Decoding for Concatenated Quantum Hamming Codes
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909989902221312 |
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| author | Zhang, Chao Wu, Zipeng Wu, Jiahui Huang, Shilin |
| author_facet | Zhang, Chao Wu, Zipeng Wu, Jiahui Huang, Shilin |
| contents | High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work, we introduce a hard-decision decoder for concatenated quantum Hamming codes with time complexity polynomial in the block length. This decoder overcomes the limitations of conventional local decoding by leveraging higher-level syndrome information to revise lower-level recovery decisions -- a strategy we refer to as bidirectional decoding. For the concatenated $[[15,7,3]]$ quantum Hamming code under independent bit-flip noise, the bidirectional decoder improves the threshold from approximately $1.56\%$ to $4.35\%$ compared with standard local decoding. Moreover, the decoder empirically preserves the full $3^{L}$ code-distance scaling for at least three levels of concatenation, resulting in substantially faster logical-error suppression than the $2^{L+1}$ scaling offered by local decoders. Our results can enhance the competitiveness of concatenated-code architectures for low-overhead fault-tolerant quantum computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09131 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bidirectional Decoding for Concatenated Quantum Hamming Codes Zhang, Chao Wu, Zipeng Wu, Jiahui Huang, Shilin Quantum Physics High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work, we introduce a hard-decision decoder for concatenated quantum Hamming codes with time complexity polynomial in the block length. This decoder overcomes the limitations of conventional local decoding by leveraging higher-level syndrome information to revise lower-level recovery decisions -- a strategy we refer to as bidirectional decoding. For the concatenated $[[15,7,3]]$ quantum Hamming code under independent bit-flip noise, the bidirectional decoder improves the threshold from approximately $1.56\%$ to $4.35\%$ compared with standard local decoding. Moreover, the decoder empirically preserves the full $3^{L}$ code-distance scaling for at least three levels of concatenation, resulting in substantially faster logical-error suppression than the $2^{L+1}$ scaling offered by local decoders. Our results can enhance the competitiveness of concatenated-code architectures for low-overhead fault-tolerant quantum computation. |
| title | Bidirectional Decoding for Concatenated Quantum Hamming Codes |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2601.09131 |