Ultrastrong coupling in a scalable design for circuit QED with superconducting flux qubits

We theoretically study a circuit quantum electrodynamics architecture with superconducting flux qubits. The qubit is coupled to the transmission line resonator by an ac current originating from the current mode of the resonator. Ultrastrong coupling can be obtained by varying the capacitance between the qubit and the resonator. We propose a scalable design where the two-qubit coupling can be achieved.