Bidirectional Decoding for Concatenated Quantum Hamming Codes

• URL: http://arxiv.org/abs/2601.09131v1
• Date: Wed, 14 Jan 2026 04:09:37 GMT
• Title: Bidirectional Decoding for Concatenated Quantum Hamming Codes
• Authors: Chao Zhang, Zipeng Wu, Jiahui Wu, Shilin Huang,
• Abstract summary: We introduce a hard-decision decoder ford quantum codes with time complexity for scaling.<n>For thed $[15,3]]$ quantum Hamming code under independent bit-flip noise, the bidirectional decoder improves the threshold.<n>Our results can enhance the competitiveness of low-overhead fault-tolerant quantum computation.
• Score: 6.26319455798863
• 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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