  We check a recent proposal [H. Goto and K. Ichimura Phys. Rev. A 70, 012305
(2004)] for controlled phase gate through adiabatic passage under the influence
of spontaneous emission and the cavity decay. We show a modification of above
proposal could be used to generate the necessary conditional phase gates in the
two-qubit Grover search. Conditioned on no photon leakage either from the
atomic excited state or from the cavity mode during the gating period, we
numerically analyze the success probability and the fidelity of the two-qubit
conditional phase gate by adiabatic passage. The comparison made between our
proposed gating scheme and a previous one shows that Goto and Ichimura's scheme
is an alternative and feasible way in the optical cavity regime for two-qubit
gates and could be generalised in principle to multi-qubit gates.
