Greenberger-Horne-Zeilinger generation protocol for N superconducting transmon qubits capacitively coupled to a quantum bus
Samuel Aldana, Ying-Dan Wang, Christoph Bruder · Physical Review B · 2011
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, $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}(XX+YY)$, 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 ${t}_{\mathrm{GHZ}}\ensuremath{\sim}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{g}}^{\ensuremath{-}1}$. 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.