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

Discrete-Time Quantum-Walk & Floquet Topological Insulators via Distance-Selective Rydberg-Interaction