Jae-weon Lee^a, Changho Kim^a, Eok-Kyun Lee^a, Jaewan Kim^b, and Soonchil Lee^b

^a Department of Chemistry and School of Molecular Science (BK21), Korea Advanced Institute of Science and Technology, Taejon, Republic of Korea
^b Department of Physics, Korea Advanced Institute of Science and Technology, Taejon, South Korea

Identifying the Bloch sphere with the Riemann sphere (the extended complex plane), we obtain relations between single qubit unitary operations and Mobius transformations on the extended complex plane.