Projective Plane and Planar Quantum Codes
نویسندگان
چکیده
Cellulations of the projective plane RP 2 define single qubit topological quantum error correcting codes since there is a unique essential cycle in H1(RP ;Z2). 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. PACS numbers: 03.67.Lx, 89.70.+c, 89.80.+h. AMS subject classification: 94Bxx, 81P99, 57M20.
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عنوان ژورنال:
- Foundations of Computational Mathematics
دوره 1 شماره
صفحات -
تاریخ انتشار 2001