  We present the two-loop virtual amplitudes for heavy-quark pair production in
light quark-antiquark annihilation and gluon fusion channels, including full
spin and color dependence. We use expansions around kinematical limits and
numerical integration to obtain results for the involved master integrals. From
these, we determine the renormalised infrared finite remainders of the
coefficients of amplitude decompositions in terms of color and spin structures.
The remainders are given in form of numerical interpolation grids supported by
expansions around the production threshold and the high energy limit. Finally,
we provide the spin density matrix, which encodes the heavy-quark spin
correlations and is sufficient for phenomenological applications. Our results
are necessary for the derivation of top-quark pair production cross sections in
hadron collisions in the narrow width approximation with
next-to-next-to-leading order accuracy in QCD.
