Projective plane and planar quantum codes
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.
 Publication:

arXiv eprints
 Pub Date:
 October 1998
 arXiv:
 arXiv:quantph/9810055
 Bibcode:
 1998quant.ph.10055F
 Keywords:

 Quantum Physics
 EPrint:
 7 pages, plain TeX, 5 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages)