Rydberg quantum simulator of topological insulators

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.