Approximate Toffoli Gate Originated from a Single Resonant Interaction of Cavity Dissipation and Atomic Spontaneous Emission

We propose a potentially practical scheme to implement an approximatethree-qubit Toffoli gate by a single resonant interaction in dissipativecavity QED in which the cavity mode decay and atomic spontaneous emissionare considered. The scheme does not require two-qubit controlled-NOT gates but uses a three-qubit phase gate and two Hadamard gates, where the approximate phase gate can be implemented by only a single dissipative resonantinteraction of atoms with the cavity mode. Discussions are made for theadvantages and the experimental feasibility of our scheme.