Simple preparation of Bell and Greenberger-Horne-Zeilinger states using ultrastrong-coupling circuit QED

The ability to entangle quantum systems is crucial for many applications in quantum technology, including quantum communication and quantum computing. Here, we propose a simple and versatile setup for deterministically creating Bell and Greenberger-Horne-Zeilinger states between photons of different frequencies in a two-step protocol. The setup consists of a quantum bit (qubit) coupled ultrastrongly to three photonic resonator modes. The only operations needed in our protocol are to put the qubit in a superposition state and then tune its frequency in and out of resonance with sums of the resonator-mode frequencies. By choosing which frequency we tune the qubit to, we select which entangled state we create. We show that our protocol can be implemented with high fidelity using feasible experimental parameters in state-of-the-art circuit quantum electrodynamics. One possible application of our setup is as a node distributing entanglement in a quantum network