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

### Abstract

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, $\tilde{g}(XX+YY)$, that can be globally controlled. Starting from a separable initial state, these interactions allow to generate a multi-qubit GHZ state within a time $t_{\text{GHZ}}\sim \tilde{g}^{-1}$. We discuss how to probe the non-local 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.Comment: 9 pages, 4 figures, accepted for publication in PR

Topics: Condensed Matter - Mesoscale and Nanoscale Physics, Quantum Physics
Year: 2011
DOI identifier: 10.1103/PhysRevB.84.134519
OAI identifier: oai:arXiv.org:1104.1022