Engineering cross resonance interaction in multi-modal quantum circuits

Existing scalable superconducting quantum processors have only nearest-neighbor coupling. This leads to reduced circuit depth, requiring large series of gates to perform an arbitrary unitary operation in such systems. Recently, multi-modal devices have been demonstrated as a promising candidate for small quantum processor units. Always on longitudinal coupling in such circuits leads to implementation of native high fidelity multi-qubit gates. We propose an architecture using such devices as building blocks for a highly connected larger quantum circuit. To demonstrate a quantum operation between such blocks, a standard transmon is coupled to the multi-modal circuit using a 3D bus cavity giving rise to small exchange interaction between the transmon and one of the modes. We study the cross resonance interaction in such systems and characterize the entangling operation as well as the unitary imperfections and cross-talk as a function of device parameters. Finally, we tune up the cross resonance drive to implement multi-qubit gates in this architecture.