We present a method for implementing an n-qubit controlled-rotation gate with three-level superconducting qubit systems in cavity quantum electrodynamics. The two logical states of a qubit are represented by the two lowest levels of each system while a higher energy level is used for the gate implementation. The method operates essentially by preparing a W state conditioned on the states of the control qubits, creating a single photon in the cavity mode, and then performing an arbitrary rotation on the states of the target qubit with the assistance of the cavity photon. It is interesting to note that the basic operational steps for implementing the proposed gate do not increase with the number of qubits n, and the gate operation time decreases as the number of qubits increases. This proposal is quite general, and can be applied to various types of superconducting devices in a cavity or coupled to a resonator.
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