Circuit design implementing longitudinal coupling: A scalable scheme for superconducting qubits

We present a circuit construction for a fixed-frequency superconducting qubit and show how it can be scaled up to a grid with strictly local interactions. The circuit QED realization we propose implements ₙ type coupling between a superconducting qubit and any number of LC resonators. The resulting longitudinal coupling is inherently different from the usual ₗ type transverse coupling, which is the one that has been most commonly used for superconducting qubits. In a grid of fixed-frequency qubits and resonators with a particular pattern of always-on interactions, coupling is strictly confined to nearest and next-nearest neighbor resonators; there is never any direct qubit-qubit coupling. We note that just a single unique qubit frequency suffices for the scalability of this scheme. The same is true for the resonators, if the resonator-resonator coupling constants are varied instead. A controlled phase gate between two neighboring qubits can be realized with microwave drives on the qubits, without affecting the other qubits. This fact is a significant advantage for the scalability of this scheme.