Codeword stabilized quantum codes: algorithm and structure
Abstract
The codeword stabilized ("CWS") quantum codes formalism presents a unifying approach to both additive and nonadditive quantum error-correcting codes (arXiv:0708.1021). This formalism reduces the problem of constructing such quantum codes to finding a binary classical code correcting an error pattern induced by a graph state. Finding such a classical code can be very difficult. Here, we consider an algorithm which maps the search for CWS codes to a problem of identifying maximum cliques in a graph. While solving this problem is in general very hard, we prove three structure theorems which reduce the search space, specifying certain admissible and optimal ((n,K,d)) additive codes. In particular, we find there does not exist any ((7,3,3)) CWS code though the linear programming bound does not rule it out. The complexity of the CWS search algorithm is compared with the contrasting method introduced by Aggarwal and Calderbank (arXiv:cs/0610159).
Cite
@article{arxiv.0803.3232,
title = {Codeword stabilized quantum codes: algorithm and structure},
author = {Isaac L. Chuang and Andrew W. Cross and Graeme Smith and John A. Smolin and Bei Zeng},
journal= {arXiv preprint arXiv:0803.3232},
year = {2015}
}
Comments
11 pages, 1 figure