  We study a one-step approach to the fast generation of
Greenberger-Horne-Zeilinger (GHZ) states in a circuit QED system with
superconducting flux qubits. The GHZ state can be generated in about 10 ns,
which is much shorter than the coherence time of flux qubits and comparable
with the time of single-qubit operation. In our proposal, a time-dependent
microwave field is applied to a superconducting transmission line resonator
(TLR) and displaces the resonator in a controlled manner, thus inducing
indirect qubit-qubit coupling without residual entanglement between the qubits
and the resonator. The design of a tunably coupled TLR circle array provides us
with the potential for extending this one-step scheme to the case of many
qubits coupled via several TLRs.
