Fast, tunable, high fidelity cZ-gates between superconducting qubits with parametric microwave control of ZZ-coupling

Future quantum information processors require tunable coupling architectures that can produce high fidelity logical gates between two or more qubits. Parametric coupling is a powerful technique for generating tunable interactions between many qubits. Here, we present a highly flexible parametric coupling scheme with superconducting qubits that provides complete removal of residual $ZZ$ coupling and the implementation of driven SWAP or SWAP-free controlled-$Z$ (c$Z$) gates. Our fully integrated, 2D on-chip coupler design is only weakly flux tunable, cancels static linear coupling between the qubits, avoids internal coupler dynamics or excitations, and is extensible to multi-qubit circuit-QED systems. Exploring gate fidelity versus gate duration allows us to maximize two-qubit gate fidelity, while providing insights into possible error sources for these gates. Randomized benchmarking over several hours reveals that the parametric SWAP c$Z$ gate achieves an average fidelity of $99.44\pm 0.09$\% in a gate duration of 70~ns and a dispersively driven parametric SWAP-free c$Z$ gate attains an average fidelity of $99.47\pm 0.07$\% in only 30~ns. The fidelity remained above this value for over 8~hours and peaked twice with a maximum of $99.67\pm 0.14$\%. Overall, our parametric approach combines versatility, precision, speed, and high performance in one compact coupler design.