Quantum convolutional codes: Practical syndrome decoder

Quantum convolutional codes are predicted by many to offer higher error correction performance than quantum block codes of equivalent encoding complexity. However, to decode a quantum convolutional code is challenging, because the decoder does not have a measurement of the received codeword (due to the quantum mechanic rule “measurement destroys quantum states”), but only a measurement of the syndrome. Although quantum Viterbi decoding (QVD) has been proposed, its high complexity makes it rather difficult to implement or simulate. Exploiting useful ideas from classical coding theory, this paper develops a practical quantum syndrome decoder (QSD) by introducing two innovations that drastically reduce the decoding complexity compared to the existing QVD. The new decoder uses an efficient linear-circuits-based mechanism to map a syndrome to a candidate vector, obviating the need of a cumbersome lookup table. It is also cleverly engineered such that only one run of the Viterbi algorithm suffices to locate the most-likely error pattern, rather than have to run many rounds as in the previous QVD algorithm. The efficiency of the new decoder allows us to simulate and present the first performance curve of a general quantum convolutional code.