  After ten years from its discovery, the Higgs boson is still under
unprecedented scrutiny. A huge theoretical effort has been invested in
modelling Higgs boson production through gluon fusion, reaching
$\text{N}^3\text{LO}$ predictions in pure QCD. This incredible theoretical
achievement makes the exact computation of sub-leading contributions, such as
mixed QCD-Electroweak corrections, necessary. I will present the analytic
calculation of the gluon- and quark-initiated two-loop four-point contributions
to such class of corrections mediated by light quarks at order $v \alpha^2
\alpha_S^{3/2}$.
