Projective Plane and Planar Quantum Codes
- 215 Downloads
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.
Unable to display preview. Download preview PDF.