Two-loop amplitudes for $qg\to Hq$ and $q\bar{q}\to Hg$ mediated by a nearly massless quark

We compute the two-loop QCD corrections to $qg\to Hq$ and $q \bar{q} \to H g$ amplitudes mediated by loops of nearly massless quarks. These amplitudes provide the last missing ingredient required to compute the NLO QCD corrections to the top-bottom interference contribution to the Higgs boson transverse momentum distribution at hadron colliders.