  Webs are combinatorial diagrams used to encode homomorphisms between
representations of Lie (super)algebras and related objects. This paper extends
the theory of webs to the quantum group of type Q. We define a monoidal
supercategory of quantum type Q webs and show it admits a full, essentially
surjective functor onto the monoidal supercategory of
$U_q(\mathfrak{q}_n)$-modules generated by the quantum symmetric powers of the
natural representation and their duals. We also show that a certain subcategory
of the web category is a ribbon category and discuss applications to the
representation theory of $U_q(\mathfrak{q}_n)$ and to invariants of oriented,
framed links.
