Generation of Greenberger-Horne-Zeilinger entangled states with three SQUID qubits: a scheme with tolerance to non-uniform device parameters

We propose a scheme for creating Greenberger-Horne-Zeilinger (GHZ) type of entangled states with three superconducting quantum interference device (SQUID) qubits in a microwave cavity. The scheme operates essentially by an auxiliary SQUID built in the cavity as a microwave photon generator, and by performing a phase shift with the aid of the cavity photon. We show that the present scheme does not require identical cavity-SQUID coupling constants for each SQUID. Therefore, our scheme can be readily implemented since neither uniform device parameters nor exact placement of SQUIDs in the cavity is required. We note that the method can in principle be applied to prepare many SQUIDs in a GHZ state. In addition, how to prepare multiple SQUIDs in W-class entangled states is discussed.