  We completely describe the tree classes of the components of the stable
Auslander-Reiten quiver of a quantum complete intersection. In particular, we
show that the tree class is always $A_{\infty}$ whenever the algebra is of wild
representation type. Moreover, in the tame case, there is one component of tree
class $\tilde{A}_{12}$, whereas all the other are of tree class $A_{\infty}$.
