  This article proposes Rydberg multi-dimensional discrete-time quantum walk
(DTQW) implementation that could ideally simulate different classes of
topological insulators. Using an 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 DTQW. Here, complicated coupling
tesselations are performed by global laser excitation. The long-range
interaction provides a new feature of designing different topologically ordered
periodic boundary conditions. Limiting the Rydberg population to 1.5
excitations, coherent QW over thousand 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.
