Title :
On the hardness of decoding quantum stabilizer codes under the depolarizing channel
Author :
Kao-Yueh Kuo ; Chung-Chin Lu
Author_Institution :
Dept. of Electr. Eng., Nat. Tsing Hua Univ., Hsinchu, Taiwan
Abstract :
We classify the complexity classes of several 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 under 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 not be possible, but this, on the other hand, strengthens the foundation of quantum code-based cryptography.
Keywords :
binary codes; channel coding; computational complexity; decoding; error statistics; linear codes; polynomials; quantum cryptography; NP-hard; classical binary linear codes; decoding error probability; decoding problems; depolarizing channel; general stabilizer codes; polynomial-time decoding algorithm; quantum code-based cryptography; quantum stabilizer codes; Complexity theory; Cryptography; Decoding; Error probability; Linear code; Measurement; Vectors;
Conference_Titel :
Information Theory and its Applications (ISITA), 2012 International Symposium on
Conference_Location :
Honolulu, HI
Print_ISBN :
978-1-4673-2521-9