Greenberger-Horne-Zeilinger generation protocol for N superconducting transmon qubits capacitively coupled to a quantum bus

We propose a circuit quantum electrodynamics (QED) realization of a protocol to generate a Greenberger-Horne-Zeilinger (GHZ) state for N superconducting transmon qubits homogeneously coupled to a superconducting transmission line resonator in the dispersive limit. We derive an effective Hamiltonian with pairwise qubit exchange interactions of the XY type, (g) over tilde (XX + YY), that can be globally controlled. Starting from a separable initial state, these interactions allow us to generate a multi-qubit GHZ state within a time t(GHZ) similar to (g) over tilde (-1). We discuss how to probe the nonlocal nature and the genuine N-partite entanglement of the generated state. Finally, we investigate the stability of the proposed scheme to inhomogeneities in the physical parameters.