  Clustering algorithms are of fundamental importance when dealing with large
unstructured datasets and discovering new patterns and correlations therein,
with applications ranging from scientific research to medical imaging and
marketing analysis. In this work, we introduce a quantum version of the density
peak clustering algorithm, built upon a quantum routine for minimum finding. We
prove a quantum speedup for a decision version of density peak clustering
depending on the structure of the dataset. Specifically, the speedup is
dependent on the heights of the trees of the induced graph of nearest-highers,
i.e., the graph of connections to the nearest elements with higher density. We
discuss this condition, showing that our algorithm is particularly suitable for
high-dimensional datasets. Finally, we benchmark our proposal with a toy
problem on a real quantum device.
