  This is the first in a sequence of papers in which we construct a quantum
version of the Kirwan map from the equivariant quantum cohomology $QH_G(X)$ of
a smooth complex projective variety X with the action of a connected complex
reductive group $G$ to the orbifold quantum cohomology $QH(X//G)$ of its
geometric invariant theory quotient $X//G$, and prove that it intertwines the
genus zero gauged Gromov-Witten potential of X with the genus zero
Gromov-Witten graph potential of $X//G$.
