Thouless pumping is a mechanism to perform the 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 Letter, 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 us 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 another 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.

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• Geometric & topological phases
• Quantum Hall effect
• Quantum engineering
• Quantum networks
• Quantum simulation
• Quantum state transfer
• Symmetry protected topological states
• Transport in networks
• Transport phenomena
• 1-dimensional spin chains
• Topological materials