Control-Z two-qubit gate on 2D Kerr cats

Bosonic encoding based on Kerr cat qubits is one of the most promising approaches for achieving high-quality, scalable multi-qubit systems that are compatible with quantum error correction for noise-biased qubits. Significant research is focused on realizing Kerr cats using superconducting circuits, and Schrödinger cat states in these works have demonstrated high lifetimes and coherence at large cat sizes. However, a comprehensive investigation into a two-qubit gate on Kerr cats, specifically to determine whether they can operate with fidelity below the fault-tolerant threshold, has not yet been fully conducted. Here, we present a protocol to perform a control-Z gate on our high-coherence planar Kerr-Cat qubit with on-chip Purcell filters.