Limits to parametric pumping in superconducting circuits

Parametric driving constitutes a promising paradigm for the development of future superconducting quantum processors. However, these systems suffer from a poorly understood effect imposing a lower limit on gate times: as the drive strength is increased, experiments show a sudden onset of leakage due to unwanted excitations. To understand this effect, we theoretically examine a parametrically driven system consisting of a qubit and a driven coupler. We identify the system parameters that govern the onset of leakage. Our study elucidates strategies for achieving faster high-fidelity gates based on parametric driving in systems composed of transmons and SNAILs.