dorsal/arxiv
View SchemaBidirectional Decoding for Concatenated Quantum Hamming Codes
| Authors | Chao Zhang, Zipeng Wu, Jiahui Wu, Shilin Huang |
|---|---|
| Categories | |
| ArXiv ID | 2601.09131vv1 |
| URL | https://arxiv.org/abs/2601.09131 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
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.
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"abstract": "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.",
"arxiv_id": "2601.09131",
"authors": [
"Chao Zhang",
"Zipeng Wu",
"Jiahui Wu",
"Shilin Huang"
],
"categories": [
"quant-ph"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "Bidirectional Decoding for Concatenated Quantum Hamming Codes",
"url": "https://arxiv.org/abs/2601.09131",
"version": "v1"
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