High-fidelity transmon-coupler-activated CCZ gate on fluxonium qubits

The Toffoli gate takes a special place in the quantum information theory. It opens up a path for efficient implementation of complex quantum algorithms. Despite tremendous progress of the quantum processors based on the superconducting qubits, realization of a high-fidelity three-qubit operation is still a challenging problem. Here, we propose a way to perform a high-fidelity $CCZ$ gate on fluxoniums capacitively connected via a transmon qubit, activated by a microwave pulse on the coupler. The main advantages of the approach are relative quickness, simplicity of calibration and significant suppression of the unwanted longitudinal $ZZ$ interaction. We provide numerical simulation of a 95-ns-long gate of higher than 99.99% fidelity with realistic circuit parameters in the noiseless model and estimate an error of about 0.25% under the conventional decoherence rates.