  We introduce and study a new mathematical structure in the generalised
(quantum) cohomology theory for Grassmannians. Namely, we relate the Schubert
calculus to a quantum integrable system known in the physics literature as the
asymmetric six-vertex model. Our approach offers a new perspective on already
established and well-studied special cases, for example equivariant K-theory,
and in addition allows us to formulate a conjecture on the so-far unknown case
of quantum equivariant K-theory.
