  We propose a superconducting qutrit-resonator chain model, and analytically
work out forms of its topological edge states. The existence of the zero-energy
mode enables to generate a state transfer between two ends of the chain,
accompanied with state flips of all intermediate qutrits, based on which
$N$-body Greenberger-Horne-Zeilinger (GHZ) states can be generated with great
robustness against disorders of coupling strengths. Three schemes of generating
large-scale GHZ states are designed, each of which possesses the robustness
against loss of qutrits or of resonators, meeting a certain performance
requirement of different experimental devices. With experimentally feasible
qutrit-resonator coupling strengths and available coherence times of qutrits
and resonators, it has a potential to generate large-scale GHZ states among
dozens of qutrits with a high fidelity. Further, we show the experimental
consideration of generating GHZ states based on the circuit QED system, and
discuss the prospect of realizing fast GHZ states.
