On the Hardnesses of Several Quantum Decoding Problems release_rfa57vhzlnhevaoomikmhrkh2y

by Kao-Yueh Kuo, Chung-Chin Lu

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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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Date   2013-07-11
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arXiv  1306.5173v2
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