  We present a way for implementing an n-qubit controlled-rotation gate with
three-level superconducting qubit systems in cavity QED. 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 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 $n$ of qubits,
and the gate operation time decreases as the number of qubits increases. This
proposal is quite general, which can be applied to various types of
superconducting devices in a cavity or coupled to a resonator.
