  The fluxonium qubit is a promising candidate for quantum computation due to
its long coherence times and large anharmonicity. We present a tunable coupler
that realizes strong inductive coupling between two heavy-fluxonium qubits,
each with $\sim50$MHz frequencies and $\sim5$ GHz anharmonicities. The coupler
enables the qubits to have a large tuning range of $\textit{XX}$ coupling
strengths ($-35$ to $75$ MHz). The $\textit{ZZ}$ coupling strength is $<3$kHz
across the entire coupler bias range, and $<100$Hz at the coupler off-position.
These qualities lead to fast, high-fidelity single- and two-qubit gates. By
driving at the difference frequency of the two qubits, we realize a
$\sqrt{i\mathrm{SWAP}}$ gate in $258$ns with fidelity $99.72\%$, and by driving
at the sum frequency of the two qubits, we achieve a $\sqrt{b\mathrm{SWAP}}$
gate in $102$ns with fidelity $99.91\%$. This latter gate is only 5 qubit
Larmor periods in length. We run cross-entropy benchmarking for over $20$
consecutive hours and measure stable gate fidelities, with
$\sqrt{b\mathrm{SWAP}}$ drift ($2 \sigma$) $< 0.02\%$ and
$\sqrt{i\mathrm{SWAP}}$ drift $< 0.08\%$.

Quantum Physics;Mesoscale and Nanoscale Physics