  We suggest a method for fast and robust quantum-state transfer in a
Su-Schrieffer-Heeger (SSH) chain, which exploits the use of
next-to-nearest-neighbour (NNN) interactions. The proposed quantum protocol
combines a rapid change in one of the topological edge states, induced by a
modulation of nearest-neighbour interactions, with a fine tuning of NNN
interactions operating a counter-adiabatic driving. The latter cancels
nonadiabatic excitations from the edge state multiplicity to the energy bands.
We use this shortcut technique for topological pumping of edge states on a
single dimerized chain and also through an interface that connects two
dimerized Su-Schrieffer-Heeger chains with different topological order. We
investigate the robustness of this protocol against both uncorrelated and
correlated disorder, and demonstrate its strong resilience to the former in
comparison to traditional adiabatic protocols for topological chains. We show
that introducing spatial correlations in the disorder increases the robustness
of the protocol, widening the range of its applicability.
