  We demonstrate a controlled-Z gate between capacitively coupled fluxonium
qubits with transition frequencies $72.3~\textrm{MHz}$ and
$136.3~\textrm{MHz}$. The gate is activated by a $61.6~\textrm{ns}$ long pulse
at the frequency between non-computational transitions $|10\rangle -
|20\rangle$ and $|11\rangle - |21\rangle$, during which the qubits complete
only $4$ and $8$ Larmor periods, respectively. The measured gate error of
$(8\pm1)\times 10^{-3}$ is limited by decoherence in the non-computational
subspace, which will likely improve in the next generation devices. Although
our qubits are about fifty times slower than transmons, the two-qubit gate is
faster than microwave-activated gates on transmons, and the gate error is on
par with the lowest reported. Architectural advantages of low-frequency
fluxoniums include long qubit coherence time, weak hybridization in the
computational subspace, suppressed residual $ZZ$-coupling rate (here
$46~\mathrm{kHz}$), and absence of either excessive parameter matching or
complex pulse shaping requirements.

Quantum Physics;Mesoscale and Nanoscale Physics;Superconductivity