Implementing multi-qubit entanglement of two-level systems inside a superconducting phase qubit

The interaction between a superconducting phase qubit and the two-level systems located inside the Josephson tunnel barrier is described by the XY model, which is naturally used to implement the i-SWAP gate. With this gate, we propose a scheme to efficiently generate multi-qubit entangled states of such two-level systems, including multipartite W state and cluster states. In particular, it is found that, with the help of the phase qubit, the entanglement witness can be used to efficiently detect the produced multi-qubit entangled states.