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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June 21, 2000. Final version recieved: April 27, 2001.
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Freedman, M., Meyer, D. Projective Plane and Planar Quantum Codes. Found. Comput. Math. 1, 325–332 (2001). https://doi.org/10.1007/s102080010013
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DOI: https://doi.org/10.1007/s102080010013