  Su-Schrieffer-Heeger (SSH) chain, serving as a paradigmatic model for
comprehending topological phases and their associated edge states, plays a
pivotal 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 non-adiabatic yet high-fidelity
transfer of edge states in a SSH chain, featuring two sublattices A and B. The
core of our approach lies in harnessing the approximate time-dependent
counter-diabatic (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 experimental
implementation and navigate computational complexities, we identify the
next-to-nearest-neighbour (NNN) hopping terms between sublattice A as dominant
CD drivings, 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 drivings identified can be seamlessly implemented across various
quantum registers, highlighting the versatility of our approach.

Quantum Physics;Mesoscale and Nanoscale Physics