  Thouless pumping is a mechanism to perform topologically protected transport
of particles by adiabatically modulating the Hamiltonian. The transported
current is a topological invariant that is intimately related to the integer
quantum Hall effect. Most of the previous works focus on topological pumping in
linear and square lattices. In this work, we theoretically propose a mechanism
to perform topological pumping in arrays of spin chains with complex
geometries. To achieve this, we consider an array where the spin chains are
coupled through their edges, which allows to split the populations to generate
superpositions of spin excitations in different spin chains. We show that due
to the topological protection, the quantum superpositions can be transported
through the array against the effect of disorder. This approach will open a new
avenue to transport excitations and correlated states with potential
applications in quantum technologies and information processing. Our ideas can
be realized in state-of-the-art quantum simulators such as cold atoms and
superconducting qubit arrays.
