Abstract: In this talk, we will define K-theoretic invariants involving certain virtual Euler characteristics of sheaves over the quot scheme of a curve. We demonstrate that these invariants fit into a topological quantum field theory valued in Z[[q]]. Additionally, we will show that the genus-0 invariants recover the small quantum K-ring of Grassmannians, offering a new approach for finding explicit formulas. In particular, we use torus localisation to obtain a Vafa-Intriligator type formula for the virtual Euler characteristics over the quot schemes. This is based on a joint work with Ming Zhang.