On the Hardnesses of Several Quantum Decoding Problems
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.
Keywords
Cite
@article{arxiv.1306.5173,
title = {On the Hardnesses of Several Quantum Decoding Problems},
author = {Kao-Yueh Kuo and Chung-Chin Lu},
journal= {arXiv preprint arXiv:1306.5173},
year = {2013}
}
Comments
There are six pages in this paper. Part of this paper was presented in the 2012 International Symposium on Information Theory and its Applications (ISITA 2012), Hawaii, USA, October 28--31, 2012