Purcell-Engineered Hybrid Coupler for Leakage-Suppressed Robust CZ Gates
We propose a Purcell-engineered notch-filter hybrid coupler for superconducting controlled-$Z$ (CZ) gates that combines coherent interaction engineering with leakage-selective dissipation. The architecture integrates a nonlinear transmon coupler with a coupled Purcell-filter and notch-resonator subsystem, providing additional control over both the coherent interaction pathways and the engineered dissipative environment. The filter branch reshapes the effective interaction pathways, while the notch resonator further tailors the frequency response of the coupled filter network and preserves strong leakage-selective dissipation. Using dressed-eigenstate analysis together with Lindblad master-equation simulations, we show that the proposed architecture substantially reduces leakage and improves the worst-case computational-state fidelity compared with an optimized single-transmon coupler while remaining robust over a broad range of coherence assumptions and device parameters. The optimized gate achieves $F_{\rm avg}=99.74\%$, $F_{\rm min}=99.62\%$, and a maximum leakage probability of $1.6\times10^{-3}$. These results demonstrate that engineered dissipation complements conventional coherent interaction engineering and provides an additional design degree of freedom for realizing robust, high-fidelity superconducting CZ gates.