  The mesoscopic scale of superconducting qubits makes their inter-spacings
comparable to the scale of wavelength of a circuit cavity field to which they
commonly couple. This comparability results in inhomogeneous coupling
strengthes for each qubit and hence asynchronous Rabi excitation cycles among
the qubits that form a quasi-lattice. We find that such inhomogeneous coupling
benefits the formation of multi-photon resonances between the single-mode
cavity field and the quasi-lattice. The multi-photon resonances lead, in turn,
to the simultaneous generation of inequivalent GHZ and W types of multipartite
entanglement states, which are not transformable to each other through local
operations with classical communications. Applying the model on the 3-qubit
quasi-lattice and using the entanglement measures of both concurrence and
3-tangle, we verify that the inhomogeneous coupling specifically promotes the
generation of the totally inseparable GHZ state.
