  We consider the extension of the transverse-momentum ($q_T$) subtraction
method at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD.
While all the $q_T$-subtraction ingredients at $q_T \neq 0$ are known in
analytical form, the third-order collinear functions and helicity-flip
functions, which contribute only at $q_T=0$, are approximated using a
prescription which uses the known result for the total Higgs boson cross
section at this order. As a first application of the third-order
$q_T$-subtraction method, we present the N$^3$LO rapidity distribution of the
Higgs boson at the LHC.
