  We analyze a high-fidelity two-qubit gate using fast flux pulses on
superconducting fluxonium qubits. The gate is realized by temporarily detuning
magnetic flux through fluxonium loop away from the half flux quantum sweet
spot. We simulate dynamics of two capacitively coupled fluxoniums during the
flux pulses and optimize the pulse parameters to obtain a highly accurate
$\sqrt{i\mathrm{swap}}$-like entangling gate. We also evaluate the effect of
the flux noise and qubit relaxation on the gate fidelity. Our results
demonstrate that the gate error remains below $10^{-4}$ for currently
achievable magnitude of the flux noise and qubit relaxation time.
