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A novel decoding algorithm is developed for general quantum convolutionalcodes. Exploiting useful ideas from classical coding theory, the new decoderintroduces two innovations that drastically reduce the decoding complexitycompared to the existing quantum Viterbi decoder. First, the new decoder usesan efficient linear-circuits-based mechanism to map a syndrome to a candidatevector, whereas the existing algorithm relies on a non-trivial lookup table.Second, the new algorithm is cleverly engineered such that only one run of theViterbi algorithm suffices to locate the most-likely error pattern, whereas theexisting algorithm must run the Viterbi algorithm many times. The efficiency ofthe proposed algorithm allows us to simulate and present the first performancecurve of a general quantum convolutional code.

Efficient ML Decoding for Quantum Convolutional Codes