Bidirectional Decoding for Concatenated Quantum Hamming Codes

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.