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

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