  We provide two two-loop amplitudes relevant for precision Higgs physics. The
first is the two-loop amplitude for Higgs boson production through gluon fusion
with exact dependence on the top quark mass up to squared order in the
dimensional regulator $\epsilon$. The second result we provide is the two-loop
amplitude for the decay of a Higgs boson into a pair of massive bottom quarks
through the Higgs-to-gluon coupling in the infinite top mass limit. Both
amplitudes are computed by finding canonical bases of master integrals, which
we evaluate explicitly in terms of harmonic polylogarithms. We obtain the bare,
renormalized and IR-subtracted amplitude and provide the results in terms of
building blocks suitable to changing renormalization schemes.
