dorsal/arxiv
View SchemaProjective plane and planar quantum codes
| Authors | Michael H. Freedman, David A. Meyer |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9810055 |
| URL | https://arxiv.org/abs/quant-ph/9810055 |
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.
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"date_created": "2026-03-02T18:02:45.187000Z",
"date_modified": "2026-03-02T18:02:45.187000Z",
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"abstract": "Cellulations of the projective plane RP^2 define single qubit topological\nquantum error correcting codes since there is a unique essential cycle in\nH_1(RP^2;Z_2). We construct three of the smallest such codes, show they are\ninequivalent, and identify one of them as Shor\u0027s original 9 qubit repetition\ncode. We observe that Shor\u0027s code can be constructed in a planar domain and\ngeneralize to planar constructions of higher genus codes for multiple qubits.",
"arxiv_id": "quant-ph/9810055",
"authors": [
"Michael H. Freedman",
"David A. Meyer"
],
"categories": [
"quant-ph"
],
"title": "Projective plane and planar quantum codes",
"url": "https://arxiv.org/abs/quant-ph/9810055"
},
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