Cavity QED Photons for Quantum Information Processing
  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. 
Moteb M. Alqahtani, Mark S. Everitt, and Barry M. Garraway
quant-ph