  We demonstrate the implementation of a spin qubit with a single Ca ion in a
micro ion trap. The qubit is encoded in the Zeeman ground state levels mJ=+1/2
and mJ=-1/2 of the S1/2 state of the ion. We show sideband cooling close to the
vibrational ground state and demonstrate the initialization and readout of the
qubit levels with 99.5% efficiency. We employ a Raman transition close to the
S1/2 - P1/2 resonance for coherent manipulation of the qubit. We observe single
qubit rotations with 96% fidelity and gate times below 5mus. Rabi oscillations
on the blue motional sideband are used to extract the phonon number
distribution. The dynamics of this distribution is analyzed to deduce the
trap-induced heating rate of 0.3(1) phonons/ms.
