(color online) Fidelities of the (a) four- and (b) five-qubit quantum controlled-phase gates versus atomic spontaneous rate γ based on the final density matrix obtained by the ideal quantum logic gate and practically final density matrix obtained through the system dynamics governed by Eq. (6) with the specific initial states , in which is used. For simplicity, we set Ω₁ = Ω₂ = Ω₃ = Ω₄ = Ω₅ = Ω, V_Rr = wΩ, Ω = qV_rr, and w = q without loss of generality.