Toffoli gate originating from a single resonant interaction with cavity QED

We propose a potentially practical scheme to implement a three-qubit Toffoli gate by a single resonant interaction in cavity QED. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the phase gate can be implemented by only a single resonant interaction of the atoms with the cavity mode. Both the situations with and without cavity decay are considered. We discuss the advantages and the experimental feasibility of our scheme.