  This article proposes the first discrete-time implementation of Rydberg
quantum walk in multi-dimensional spatial space that could ideally simulate
different classes of topological insulators. Using distance-selective
exchange-interaction between Rydberg excited atoms in an atomic array with dual
lattice-constants, the new setup operates both coined and coin-less models of
discrete-time quantum walk (DTQW). Here, complicated coupling tessellations are
performed by a global laser that exclusively excites the site at the
anti-blockade region. The long-range interaction provides a new feature of
designing different topologically ordered periodic boundary conditions.
Limiting the Rydberg population to two excitations, coherent QW over hundreds
of lattice sites and steps are achievable with the current technology. These
features would improve the performance of this quantum machine in running the
quantum search algorithm over topologically ordered databases as well as
diversifying the range of topological insulators that could be simulated.
