Projective plane and planar quantum codes

Details Projective plane and planar quantum codes Projective plane and planar quantum codes

1998-10-18

arxiv.org/abs/quant-ph/9810055v1

Physics

Quantum Physics

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

Scientific paper

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.

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