  We consider bosonic condensates of exciton-polaritons optically confined in
elliptical traps. A superposition of two non-degenerated \textit{p}-type states
of the condensate oriented along the two main axes of the trap is represented
by a point on a Bloch sphere, being considered as an optically tunable qubit.
We describe a set of universal single-qubit gates resulting in a controllable
shift of the Bloch vector by means of an auxiliary laser beam. Moreover, we
consider interaction mechanisms between two neighboring traps that enable
designing two-qubit operations such as CPHASE, \textit{i}SWAP, and CNOT gates.
Both the single- and two-qubit gates are analyzed in the presence of error
sources in the context of polariton traps, such as pure dephasing and
spontaneous relaxation mechanisms, leading to a fidelity reduction of the final
qubit states and quantum concurrence, as well as the increase of Von Neumann
entropy. We also discuss the applicability of our qubit proposal in the context
of DiVincenzo's criteria for the realization of local quantum computing
processes. Altogether, the developed set of quantum operations would pave the
way to the realization of a variety of quantum algorithms in a planar
microcavity with a set of optically induced elliptical traps.
