  We compute the three-loop helicity amplitudes for $q\bar{q} \to gg$ and its
crossed partonic channels, in massless QCD. Our analytical results provide a
non-trivial check of the color quadrupole contribution to the infrared poles
for external states in different color representations. At high energies, the
$qg \to qg$ amplitude shows the predicted factorized form from Regge theory and
confirms previous results for the gluon Regge trajectory extracted from $qq'
\to qq'$ and $gg \to gg$ scattering.
