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Hybrid quantum gates have recently drawn considerable attention. They playsignificant roles in connecting quantum information processors with qubits ofdifferent encoding and have important applications in the transmission ofquantum states between a quantum processor and a quantum memory. In this work,we propose a single-step implementation of a multi-target-qubit controlled-NOTgate with one superconducting (SC) qubit simultaneously controlling $n$ targetcat-state qubits. In this proposal, the gate is implemented with $n$ microwavecavities coupled to a three-level SC qutrit. The two logic states of thecontrol SC qubit are represented by the two lowest levels of the qutrit, whilethe two logic states of each target cat-state qubit are represented by twoquasi-orthogonal cat states of a microwave cavity. This proposal operatesessentially through the dispersive coupling of each cavity with the qutrit. Thegate realization is quite simple because it requires only a single-stepoperation. There is no need of applying a classical pulse or performing ameasurement. The gate operation time is independent of the number of targetqubits, thus it does not increase as the number of target qubits increases.Moreover, because the third higher energy level of the qutrit is not occupiedduring the gate operation, decoherence from the qutrit is greatly suppressed.As an application of this hybrid multi-target-qubit gate, we further discussthe generation of a hybrid Greenberger-Horne-Zeilinger (GHZ) entangled state ofSC qubits and cat-state qubits. As an example, we numerically analyze theexperimental feasibility of generating a hybrid GHZ state of one SC qubit andthree cat-state qubits within present circuit QED technology.

physical review. a/physical review, a

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