  Based on a multimode multilevel Jaynes-Cummings model and multiphoton
resonance theory, a set of universal two- and three-qubit gates, namely the
iSWAP and the Fredkin gates, has been realized where dual-rail qubits are
encoded in cavities. In this way the information has been stored in cavities
and the off-resonant atomic levels have been eliminated by the semi-classical
theory of an effective two-level Hamiltonian. A further semi-classical model,
namely the spin-$J$ model, has been introduced so that a complete population
inversion for levels of interest has been achieved and periodic multilevel
multiphoton models have been performed. The combination of the two
semi-classical models has been employed to address two-level, three-level,
four-level, and even five-level configurations. The impact of decoherence
processes on the fidelity of the iSWAP and the Fredkin gates has been studied.
