  We propose an all optical quantum computation scheme, with trapped electron
spin qubits, using their Coulomb exchange interaction with optically excited
microcavity exciton-polaritons. This paper describes a single qubit rotation,
which together with two-qubit controlled-z gate presented in PRB 85, 241403(R)
(2012), form a set of universal logic gates. The errors due to finite cavity
lifetime and incorrect orientation of the rotation axis are minimized by
optimizing pump pulse parameters. With projective homodyne phase measurement
and initialization, our scheme is a promising candidate for the physical
realization of a universal quantum computer.
