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Parametric coupling is a powerful technique for generating tunableinteractions between superconducting circuits using only microwave tones. Here,we present a highly flexible parametric coupling scheme demonstrated with twotransmon qubits, which can be employed for multiple purposes, including theremoval of residual $ZZ$ coupling and the implementation of driven swap orswap-free controlled-$Z$ (c$Z$) gates. Our fully integrated coupler design isonly weakly flux tunable, cancels static linear coupling between the qubits,avoids internal coupler dynamics or excitations, and operates with rf-pulses.We show that residual $ZZ$ coupling can be reduced with a parametric dispersivetone down to an experimental uncertainty of 5.5 kHz. Additionally, randomizedbenchmarking reveals that the parametric swap c$Z$ gate achieves a fidelity of99.4% in a gate duration of 60 ns, while the dispersive parametric swap-freec$Z$ gate attains a fidelity of 99.5% in only 30 ns. We believe this is thefastest and highest fidelity gate achieved with on-chip parametric coupling todate. We further explore the dependence of gate fidelity on gate duration forboth p-swap and p-swap-free c$Z$ gates, providing insights into the possibleerror sources for these gates. Overall, our findings demonstrate a versatility,precision, speed, and high performance not seen in previous parametricapproaches. Finally, our design opens up new possibilities for creating larger,modular systems of superconducting qubits.

Versatile parametric coupling between two statically decoupled transmon qubits