  We calculate the complete soft-gluon corrections for the production of
colorless final states through N$^3$LO in single-particle-inclusive kinematics.
We present explicit analytical results and use them to study higher-order QCD
corrections for the production of a heavy charged Higgs pair ($H^+ H^-$) via
quark-antiquark annihilation in the Two-Higgs-Doublet Model at LHC energies. We
calculate the NNLO soft-gluon and virtual QCD corrections as well as the
N$^3$LO soft-gluon corrections to the total cross section and the charged-Higgs
rapidity distribution. This is the first calculation of complete N$^3$LO
soft-gluon corrections for a process in single-particle-inclusive kinematics,
and the results can be applied to other processes with colorless final states.
