Optimal fluxonium parameters for capacitive cross-resonance gate

Fluxonium qubits have recently demonstrated millisecond long coherence times enabled by their reduced susceptibility to dielectric losses. This resilience comes from its low qubit frequencies and suppressed charge matrix elements. However, this characteristic also reduces the qubit-qubit coupling between capacitively coupled fluxoniums, which poses a challenge for entangling gates. In this work, we study an architecture for cross-resonance gates with fluxonium qubits. We aim to obtain the fastest gate speed given a low target residual ZZ rate. Using a semi-analytic approach, we find energy design parameters for control and target qubits which generally allows for CNOT gate durations around 150 ns with a 50 kHz residual ZZ under strong charge driving. We further provide estimates of frequency collision windows around harmful control-target and control-spectator transitions.