  Topological pumping and duality transformations are paradigmatic concepts in
condensed matter and statistical mechanics. In this paper, we extend the
concept of topological pumping of particles to topological pumping of quantum
correlations. We propose a scheme to find pumping protocols for
highly-correlated states by mapping them to uncorrelated ones. We show that one
way to achieve this is to use dualities, because they are non-local
transformations that preserve the topological properties of the system. By
using them, we demonstrate that topological pumping of kinks and cluster-like
excitations can be realized. We find that the entanglement of these
highly-correlated excitations is strongly modified during the pumping process
and the interactions enhance the robustness against disorder. Our work paves
the way to explore topological pumping beyond the notion of particles and opens
a new avenue to investigate the relation between correlations and topology.
