A simplify proposal for realizing multiqubit tunable phase gate in circuit QED

We propose a scheme to realize multiqubit tunable phase gate in a circuit QED setup where two resonators each coupling with a qudit are interconnected to a common qudit (d = 4). In this proposal, only two levels of each qudit serve as the logical states and other two levels are used for the gate realization. The proposal is efficient and simple because it requires only one step, no adjustments of the qudit level spacings and resonator mode frequency are needed during the whole process. Only a classical microwave pulse is needed to drive the central coupler qudit, no matter how many qudits involve, which significantly reduces experimental difficulty. In non-resonant case, the tunable phase gate can be achieved readily, while under the resonant condition a {\pi}-phase gate can be realized after a full cycle of Rabi oscillation where the gate speed is rather fast due to the resonant interaction. We have shown that the resulting effective dynamics allows for the creation of high fidelity phase gate. The influence of various decoherence processes such as the decay of the resonator mode, and the relaxation of the qudits is investigated. Moreover, the proposed scheme can be easily generalized to realize N-qubit phase gate.