Two simple schemes for implementing Toffoli gate via atom--cavity field interaction in cavity quantum electrodynamics

This paper proposes two schemes for implementing three-qubit Toffoli gate with an atom (as target qubit) sent through a two-mode cavity (as control qubits). The first scheme is based on the large-detuning atom--cavity field interaction and the second scheme is based on the resonant atom-field interaction. Both the situations with and without cavity decay and atomic spontaneous emission are considered. The advantages and the experimental feasibility of these two schemes are discussed.