  Homology is a tool in topological data analysis which measures the shape of
the data. In many cases, these measurements translate into new insights which
are not available by other means. To compute homology, we rely on mathematical
constructions which scale exponentially with the size of the data. Therefore,
for large point clouds, the computation is infeasible using classical
computers. In this paper, we present a quantum annealing pipeline for
computation of homology of large point clouds. The pipeline takes as input a
graph approximating the given point cloud. It uses quantum annealing to compute
a clique covering of the graph and then uses this cover to construct a
Mayer-Vietoris complex. The pipeline terminates by performing a simplified
homology computation of the Mayer-Vietoris complex. We have introduced three
different clique coverings and their quantum annealing formulation. Our
pipeline scales polynomially in the size of the data, once the covering step is
solved. To prove correctness of our algorithm, we have also included tests
using D-Wave 2X quantum processor.
