phases, yielding a quantum superposition called a Schrödinger cat state. Universal quantum computing with KPOs requires three kinds of quantum gates: Rz,Rx, and Rzz gates. We theoretically propose a two-qubit gate Rzz for highly detuned KPOs. In the proposed scheme, we add another two-photon drive for the first KPO. This leads to the Rzz gate based on the driving of the second KPO depending on the first-KPO state, which we call „conditional driving.“ First, we perform simulations using a conventional KPO Hamiltonian derived from a superconducting-circuit model under some approximations and evaluate the gate fidelity. Next, we also perform numerical simulations of the two-qubit gate using the superconducting-circuit model without the approximations. The simulation results indicate that two-qubit gates can be implemented with high fidelity (>99.9%) for rotation angles required for universality.