Right-sizing fluxonium against charge noise

Fluxonium qubits employ a chain of $N$ Josephson junctions in series. We investigate how the charge-noise induced coherence time ${T}_{2}$ of the qubit depends upon $N$, holding fixed the chain's effective capacitance and inductance. The pure dephasing rate decreases with $N$, but the relaxation rate increases. As a result, ${T}_{2}$ achieves a maximum. The optimal $N$ can be much smaller than the number typically chosen in experiments, implying that fluxonium qubits can be significantly simplified without compromising performance.