Projective plane and planar quantum codes
Quantum Physics
2007-05-23 v1
Abstract
Cellulations of the projective plane RP^2 define single qubit topological quantum error correcting codes since there is a unique essential cycle in H_1(RP^2;Z_2). We construct three of the smallest such codes, show they are inequivalent, and identify one of them as Shor's original 9 qubit repetition code. We observe that Shor's code can be constructed in a planar domain and generalize to planar constructions of higher genus codes for multiple qubits.
Keywords
Cite
@article{arxiv.quant-ph/9810055,
title = {Projective plane and planar quantum codes},
author = {Michael H. Freedman and David A. Meyer},
journal= {arXiv preprint arXiv:quant-ph/9810055},
year = {2007}
}
Comments
7 pages, plain TeX, 5 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages)