Preparation of entangled W states with cat-state qubits in circuit QED

Cat-state qubits (qubits encoded with cat states) have recently attracted much attention because of their enhanced lifetimes with quantum error correction. We here consider a circuit QED system consisting of three superconducting qutrits, each coupled to an individual cavity but all coupled to a common cavity. We show that entangled W states of three cat-state qubits hosted by the three individual cavities can be prepared with only a few basic operations. The higher energy level of the qutrits is not occupied; thus, decoherence from this level of the qutrits is greatly suppressed. In addition, the W states can be prepared deterministically. Numerical simulations show that high-fidelity production of the W states of three cat-state qubits is feasible with current circuit QED technology. This proposal is quite general and can be applied to create the proposed W states, with each cavity being a microwave or optical cavity and each qutrit being a three-level natural or artificial atom.