Floquet theory for effective gate Hamiltonian and crosstalk in a tunable coupling superconducting circuit*

The realization of high-fidelity quantum gates involves a multitude of parameters governing important properties of the system, such as the gate rate, leakage and the extent of spurious interactions. One therefore needs to carefully choose these parameters to optimize the gate fidelity and speed. Numerically, this can be a resource intensive process as it implies simulating the gate dynamics for each set of device parameters. Here, we present a method to extract the interaction rates directly from Floquet spectrum generated by the drive without having to run dynamical simulations. We apply this technique to a two-qubit entangling parametric gate to optimize the device parameters in order to cancel the static ZZ interaction and minimize the gate time. We show that our method agrees with unitary dynamics simulations and perturbation theory.