  The Su-Schrieffer-Heeger (SSH) chain, which serves as a paradigmatic model
for comprehending topological phases and their associated edge states, plays an
essential role in advancing our understanding of quantum materials and quantum
information processing and technology. In this paper, we introduce a hybrid
analog-digital protocol designed for the nonadiabatic yet high-fidelity
transfer of edge states in an SSH chain, featuring two sublattices, A and B.
The core of our approach lies in harnessing the approximate time-dependent
counterdiabatic (CD) interaction, derived from adiabatic gauge potentials.
However, to enhance transfer fidelity, particularly in long-distance chains,
higher-order nested commutators become crucial. To simplify the experimental
implementation and navigate computational complexities, we identify the
next-to-nearest-neighbor hopping terms between sublattice A sites as dominant
CD driving and further optimize them by using variational quantum circuits.
Through digital quantum simulation, our protocol showcases the capability to
achieve rapid and robust solutions, even in the presence of disorder. This
analog-digital transfer protocol, an extension of quantum control methodology,
establishes a robust framework for edge-state transfer. Importantly, the
optimal CD driving identified can be seamlessly implemented across various
quantum registers, highlighting the versatility of our approach.
