Realization of High-Fidelity CZ and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Z</mml:mi><mml:mi>Z</mml:mi></mml:math> -Free iSWAP Gates with a Tunable Coupler

High-fidelity two-qubit gates at scale are a key requirement to realize the full promise of quantum computation and simulation. The advent use coupler elements tunably control interactions has improved operational fidelity in many-qubit systems by reducing parasitic coupling frequency crowding issues. Nonetheless, gate errors still limit capability near-term applications. reason, part, is existing framework for tunable couplers based on dispersive approximation does not fully incorporate three-body multi-level dynamics, which essential addressing coherent leakage longitudinal ($ZZ$) during gates. Here, we present systematic approach that goes beyond exploit engineered level structure optimize its control. Using this approach, experimentally demonstrate CZ $ZZ$-free iSWAP with interaction fidelities $99.76 \pm 0.07$% $99.87 0.23$%, respectively, close their $T_1$ limits.