Scheme for constructing graphs associated with stabilizer quantum codes
Abstract
We propose a systematic scheme for the construction of graphs associated with binary stabilizer codes. The scheme is characterized by three main steps: first, the stabilizer code is realized as a codeword-stabilized (CWS) quantum code; second, the canonical form of the CWS code is uncovered; third, the input vertices are attached to the graphs. To check the effectiveness of the scheme, we discuss several graphical constructions of various useful stabilizer codes characterized by single and multi-qubit encoding operators. In particular, the error-correcting capabilities of such quantum codes are verified in graph-theoretic terms as originally advocated by Schlingemann and Werner. Finally, possible generalizations of our scheme for the graphical construction of both (stabilizer and nonadditive) nonbinary and continuous-variable quantum codes are briefly addressed.
Cite
@article{arxiv.1407.2777,
title = {Scheme for constructing graphs associated with stabilizer quantum codes},
author = {Carlo Cafaro and Damian Markham and Peter van Loock},
journal= {arXiv preprint arXiv:1407.2777},
year = {2014}
}
Comments
42 pages, 12 figures