  We present a review on the progress in the understanding and characterization
of holonomy and topology of a discrete-time quantum walk architecture,
consisting of a unitary step given by a sequence of two non-commuting rotations
in parameter space \cite{Puentesarxiv}. Unlike other similar systems recently
studied in detail in the literature, this system does not present continous 1D
topological boundaries, it only presents a discrete number of Dirac points
where the quasi- energy gap closes. At these discrete points the topological
winding number is not defined. Therefore, such discrete points represent
topological boundaries of dimension zero, and they endow the system with a
non-trivial topology. We illustrate the non-trivial character of the system by
calculating the Zak phase. We also propose a suitable experimental scheme to
implement these ideas, and we present preliminary experimental data.
