  In this work, we are interested on the implementation of single-qubit gates
on coupled Bose-Einstein condensates (BECs). The system, a feasible candidate
for a qubit, consists on condensed atoms of different hyperfine levels coupled
by a two-photon transition. It is well established that the dynamics of coupled
BECs can be described by the two-mode Hamiltonian which takes into account the
confinement potential of the trap and the effects of collisions associated with
each condensate. Other effects, as collisions between atoms belonging to
different BECs and detuning are included in this approach. We demonstrate how
to implement two types of quantum logic gates: \textit{transfer-population}
gates (NOT, $\hat{Y}$, and Hadamard), which require inversion of population
between hyperfine levels, and \textit{phase} gates ($\hat{Z}$, $\hat{S}$, and
$\hat{T}$), which require self-trapping. We also discuss the experimental
feasibility, checking the robustness of quantum gates against variations of
physical parameters out of the ideal conditions for implementation of each
quantum logic gate.
