Implementation of a multiqubit phase gate with one qubit simultaneously controlling n qubits in the ion-trap system

In this paper, we present a scheme for implementing a multiqubit phase gate with one control qubit simultaneously controlling n target qubits in the ion-trap system. In our scheme, there is no energy exchange between the internal and external degrees of freedom in the course of operation, and the vibrational mode is only virtually excited. The system is insensitive to changes in the vibrational motion. The proposed scheme is experimentally feasible based on the present ion-trap techniques.