  We generalize the asymptotic faithfulness of the skein quantum $SU(2)$
representations of mapping class groups of orientable closed surfaces to skein
$SU(3)$. Skein quantum representations of mapping class groups are different
from the Reshetikin-Turaev ones from quantum groups or geometric quantization
because they are given by different modular tensor categories. We conjecture
asymptotic faithfulness holds for skein quantum $G$ representations when $G$ is
a simply-connected simple Lie group. The difficulty for such a generalization
lies in the lack of an explicit description of the fusion spaces with
multiplicities to define an appropriate complexity of state vectors.
