Upper speed limit on parametric gates in Josephson junction-based circuits (part II)

Parametric driving of a qubit coupler presents a convenient way to control systems of superconducting qubits. This setup aims to realize fast and efficient single- or multi-qubit gates, where gate speeds ideally increase with drive strength. However, experiments reveal that an increase in drive strength eventually leads to a sudden proliferation of excitations in the coupler. This generally limits the maximum speed of parametric gates. To study this drive-induced breakdown, we consider a strongly and off-resonantly driven transmon. Using full numerical simulations of the system's dynamics, we observe a crossover region in drive strength beyond which the transmon occupies highly-excited states. We show how to locate the onset of breakdown, which agrees well with the experimental data. Moreover, we show that the sudden excitations can be understood using the tools previously developed to describe the breakdown of dispersive readout [Phys. Rev. X 14, 041023 (2024)]. Our work opens pathways to the optimization of qubit couplers for maximizing gate speeds.