  Topological data analysis is a rapidly developing area of data science where
one tries to discover topological patterns in data sets to generate insight and
knowledge discovery. In this project we use quantum walk algorithms to discover
features of a data graph on which the walk takes place. This can be done faster
on quantum computers where all paths can be explored using superposition. We
begin with simple walks on a polygon and move up to graphs described by higher
dimensional meshes. We use insight from the physics description of quantum
walks defined in terms of probability amplitudes to go from one site on a graph
to another distant site and show how this relates to the Feynman propagator or
Kernel in the physics terminology. Our results from quantum computation using
IBM's Qiskit quantum computing software were in good agreement with those
obtained using classical computing methods.
