  We study the quantum walk on the off-diagonal Aubry-Andr\'e-Harper (AAH)
lattice with periodic modulation using a digital quantum computer. We
investigate various initial states at the single-particle level, considering
different hopping modulation strengths and phase factors. Initiating the
quantum walk with a particle at the lattice edge reveals the robustness of the
edge state, attributed to the topological nature of the AAH model, and displays
the influence of the phase factor on this edge state. On the other hand, when
the quantum walk begins with a particle in the lattice bulk, we observe a
repulsion of the bulk walker from the edge, especially under strong hopping
modulation. Furthermore, we extend our investigation to the quantum walk of two
particles with nearest-neighbour (NN) interaction. We show the repulsion effect
in the quantum walk when two walkers originate from the edge and bulk of the
lattice due to the interaction. Additionally, when two particles are positioned
at NN sites and subjected to strong hopping modulation strength, they exhibit
localization in the presence of interaction. We analyze these phenomena by
examining physical quantities such as density evolution, two-particle
correlation, and participation entropy, and discuss their potential
applications in quantum technologies.
