  We study the genus-zero Gromov-Witten theory of two natural resolutions of
determinantal varieties, termed the PAX and PAXY models. We realize each
resolution as lying in a quiver bundle, and show that the respective quiver
bundles are related by a quiver mutation. We prove that generating functions of
genus-zero Gromov-Witten invariants for the two resolutions are related by a
specific cluster change of variables. Along the way, we obtain a quantum
Thom-Porteous formula for determinantal varieties and prove a Seiberg-like
duality statement for certain quiver bundles.
