Two Fluxonium CZ Gate using a Transmon Coupler

There have been increasing efforts to improve the coherence times and gate fidelities for superconducting qubits. Recently, fluxonium qubits have been gaining atention due to its large anharmonicity, millisecond coherence times, and higher gate fidelities. In this work we study two fluxoniums capacitively coupled by a flux-tunable transmon. We implement a CZ gate by selectively driving the transmon levels. Specifically, we cycle the transmon-population through non-computational states conditional on the state of the fluxoniums, thus, accumulating a conditional phase. Our circuit is designed to have optimal frequency selectivity. Using numerical simulations, we demonstrate high fidelities, low leakage, and very low residual ZZ-interaction. We will also present our first results on our experimental implementation.