Single-step implementation of a hybrid controlled-not gate with one superconducting qubit simultaneously controlling multiple target cat-state qubits

Hybrid quantum gates have recently drawn considerable attention. They play significant roles in connecting information processors with qubits of different encoding and important applications the transmission states between a processor memory. In this work, we propose single-step implementation multi-target-qubit controlled-NOT gate one superconducting (SC) qubit simultaneously controlling $n$ target cat-state qubits. proposal, is implemented microwave cavities coupled to three-level SC qutrit. The two logic control are represented by lowest levels qutrit, while each quasi-orthogonal cat cavity. This proposal operates essentially through dispersive coupling cavity realization quite simple because it requires only operation. There no need applying classical pulse or performing measurement. operation time independent number qubits, thus does not increase as increases. Moreover, third higher energy level qutrit occupied during operation, decoherence from greatly suppressed. As an application hybrid gate, further discuss generation Greenberger-Horne-Zeilinger (GHZ) entangled state example, numerically analyze experimental feasibility generating GHZ three within present circuit QED technology.