  We present an algorithm for quantum-assisted cluster analysis (QACA) that
makes use of the topological properties of a D-Wave 2000Q quantum processing
unit (QPU). Clustering is a form of unsupervised machine learning, where
instances are organized into groups whose members share similarities. The
assignments are, in contrast to classification, not known a priori, but
generated by the algorithm. We explain how the problem can be expressed as a
quadratic unconstrained binary optimization (QUBO) problem, and show that the
introduced quantum-assisted clustering algorithm is, regarding accuracy,
equivalent to commonly used classical clustering algorithms. Quantum annealing
algorithms belong to the class of metaheuristic tools, applicable for solving
binary optimization problems. Hardware implementations of quantum annealing,
such as the quantum annealing machines produced by D-Wave Systems, have been
subject to multiple analyses in research, with the aim of characterizing the
technology's usefulness for optimization, sampling, and clustering. Our first
and foremost aim is to explain how to represent and solve parts of these
problems with the help of the QPU, and not to prove supremacy over every
existing classical clustering algorithm.
