Fast parametric two-qubit gates with suppressed residual interaction using a parity-violated superconducting qubit

We demonstrate fast two-qubit gates using a parity-violated superconducting qubit consisting of a capacitively-shunted asymmetric Josephson-junction loop under a finite magnetic flux bias. The second-order nonlinearity manifesting in the qubit enables the interaction with a neighboring single-junction transmon qubit via first-order inter-qubit sideband transitions with Rabi frequencies up to 30~MHz. Simultaneously, the unwanted static longitudinal~(ZZ) interaction is eliminated with ac Stark shifts induced by a continuous microwave drive near-resonant to the sideband transitions. The average fidelities of the two-qubit gates are evaluated with randomized benchmarking as 0.967, 0.951, 0.956 for CZ, iSWAP and SWAP gates, respectively.