Topological insulators are challenging to synthesize, and limited in topological phases accessible with solid-state materials. This has motivated the search for topological phases on the systems that simulate the same principles underlying topological insulators. Discrete time quantum walks (DTQW) have been proposed for making Floquet topological insulators (FTI). This periodically driven system simulates an effective (Floquet) Hamiltonian that is topologically nontrivial. This system replicates the effective Hamiltonians from all universal classes of 1- to 3-D topological insulators. Interestingly, topological properties of Floquet topological insulators could be controlled via an external periodic drive rather than an external magnetic field. An atomic lattice empowered by distance selective Rydberg interaction could simulate different classes of FTI over a couple of hundred sites and steps in 1, 2 or 3 dimensions. The long-range interaction allows designing topologically ordered periodic boundary conditions, further enriching the realizable topological phases.