  Persistent homology, a powerful mathematical tool for data analysis,
summarizes the shape of data through tracking topological features across
changes in different scales. Classical algorithms for persistent homology are
often constrained by running times and memory requirements that grow
exponentially on the number of data points. To surpass this problem, two
quantum algorithms of persistent homology have been developed based on two
different approaches. However, both of these quantum algorithms consider a data
set in the form of a point cloud, which can be restrictive considering that
many data sets come in the form of time series. In this paper, we alleviate
this issue by establishing a quantum Takens's delay embedding algorithm, which
turns a time series into a point cloud by considering a pertinent embedding
into a higher dimensional space. Having this quantum transformation of time
series to point clouds, then one may use a quantum persistent homology
algorithm to extract the topological features from the point cloud associated
with the original times series.
