Fast $R_{xx}(\theta)$ gate operations in a tunable inductive coupler between fluxonium qubits

We propose a gate scheme for $R_{xx}(\theta)$ gates on the tunable inductive coupler between fluxonium qubits driven by the coupler-flux. Compared to the previously demonstrated gate schemes, which use a parametric drive and are limited to a weak-driving regime where the two frequency components $\omega_A \pm \omega_B$ are resolved, our gate scheme can achieve a strong-driving regime, up to which the error budget from leakage dynamics exceeds that from the decoherence. We provide a master-equation simulation to estimate the speed-optimal gate fidelity under realistic conditions, including the effects of leakage, crosstalk, dissipation, and 1/f flux noise.