Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) optical qubits is a fascinating area of quantum science and technology, because such hybrid entanglement is a key resource for building hybrid quantum networks and interconnecting quantum processors employing different qubit encodings. In this work, we propose a scheme to create a hybrid Greenberger-Horne-Zeilinger–type (GHZ-type) entangled state of a single DV optical qubit and $n$ CV optical qubits, utilizing $(n+1)$ microwave cavities coupled to a superconducting flux qutrit. The two logic states of a DV optical qubit here are represented by the vacuum state and the single-photon state of a cavity, while the two logic states of a CV optical qubit are indicated by the two coherent states of a cavity. The GHZ state preparation protocol requires only a few basic operations, significantly reducing circuit resources by utilizing a single flux qutrit as the coupler. Since the third energy level of the qutrit remains unpopulated during the operation, decoherence from higher levels is significantly suppressed. Moreover, the total operation time is independent of the number of microwave cavities, and the GHZ state is deterministically generated since no measurement is made. As an example, our numerical simulation demonstrates that high-fidelity generation of a hybrid four-cavity GHZ state is feasible with present circuit quantum electrodynamics (QED) technology. This proposal is quite universal and can be applied to other physical systems, such as microwave or optical cavities, which are coupled to an artificial or a natural atom.

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• Quantum information with hybrid systems
• Superconducting qubits