On the Hardnesses of Several Quantum Decoding Problems
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by
Kao-Yueh Kuo, Chung-Chin Lu
2013
Abstract
We classify the time complexities of three important decoding problems for
quantum stabilizer codes. First, regardless of the channel model, quantum
bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece
and Tilborg did for classical binary linear codes in 1978. Then over the
depolarizing channel, the decoding problems for finding a most likely error and
for minimizing the decoding error probability are also shown to be NP-hard. Our
results indicate that finding a polynomial-time decoding algorithm for general
stabilizer codes may be impossible, but this, on the other hand, strengthens
the foundation of quantum code-based cryptography.
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