We propose a one-step scheme to implement a multiqubit controlled phase gate of one qubit simultaneously controlling multiple qubits with three-level atoms at distant nodes in coupled cavity arrays. The selective qubit-qubit couplings are achieved by
adiabatically eliminating the atomic excited states and photonic states and the required phase shifts between the control qubit and any target qubit can be realized through suitable choices of the parameters of the external fields. Moreover, the effective model is robust against decoherence because neither the atoms nor the field modes during the gate operation are excited, leading to a useful step toward scalable quantum computing networks.
