Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit

We discuss how to generate entangled coherent states of four microwave resonators (a.k.a. cavities) coupled by a three-level superconducting device (qutrit). We also show that a Greenberger-Horne-Zeilinger (GHZ) state of four superconducting qubits embedded in four different resonators can be created with this scheme. In principle, the proposed method can be extended to create an entangled coherent state of n resonators and to prepare a (GHZ) state of n qubits distributed over n cavities in a quantum network. In addition, it is noted that four resonators coupled by a coupler qutrit may be used as a basic circuit block to build a two-dimensional quantum network, which is useful for scalable quantum information processing.