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Discrete-time quantum walks allow Floquet topological insulator materials tobe explored using controllable systems such as ultracold atoms in opticallattices. By numerical simulations, we study the robustness of topologicallyprotected edge states in the presence of decoherence in one- andtwo-dimensional discrete-time quantum walks. We also develop a simpleanalytical model quantifying the robustness of these edge states against eitherspin or spatial dephasing, predicting an exponential decay of the population oftopologically protected edge states. Moreover, we present an experimentalproposal based on neutral atoms in spin-dependent optical lattices to realizespatial boundaries between distinct topological phases. Our proposal relies ona new scheme to implement spin-dependent discrete shift operations in atwo-dimensional optical lattice. We analyze under realistic decoherenceconditions the experimental feasibility of observing unidirectional,dissipationless transport of matter waves along boundaries separating distincttopological domains.

Robustness of topologically protected edge states in quantum walk experiments with neutral atoms