Error analysis in suppression of unwanted qubit interactions for a parametric gate in a tunable superconducting circuit

We experimentally demonstrate a parametric iswap gate in a superconducting circuit based on a tunable coupler for achieving a continuous tunability to eliminate unwanted qubit interactions. We implement the two-qubit iswap gate by applying a fast-flux bias modulation pulse on the coupler to turn on parametric exchange interaction between computational qubits. The controllable interaction can provide an extra degree of freedom to verify the optimal condition for constructing the parametric gate. Aiming to fully investigate error sources of the two-qubit gates, we perform quantum process tomography measurements and numerical simulations as varying static $ZZ$ coupling strength. We quantitatively calculate the dynamic $ZZ$ coupling parasitizing in two-qubit gate operation, and extract the particular gate error from the decoherence, dynamic $ZZ$ coupling, and high-order oscillation terms. Our results reveal that the main gate error comes from the decoherence, while the increase in the dynamic $ZZ$ coupling and high-order oscillation error degrades the parametric gate performance. This approach, which has not yet been previously explored, provides a guiding principle to improve gate fidelity of a parametric iswap gate by suppression of the unwanted qubit interactions. This controllable interaction, together with the parametric modulation technique, is desirable for crosstalk-free multiqubit quantum circuits and quantum simulation applications.