  Clustering algorithms are at the basis of several technological applications,
and are fueling the development of rapidly evolving fields such as machine
learning. In the recent past, however, it has become apparent that they face
challenges stemming from datasets that span more spatial dimensions. In fact,
the best-performing clustering algorithms scale linearly in the number of
points, but quadratically with respect to the local density of points. In this
work, we introduce qLUE, a quantum clustering algorithm that scales linearly in
both the number of points and their density. qLUE is inspired by CLUE, an
algorithm developed to address the challenging time and memory budgets of Event
Reconstruction (ER) in future High-Energy Physics experiments. As such, qLUE
marries decades of development with the quadratic speedup provided by quantum
computers. We numerically test qLUE in several scenarios, demonstrating its
effectiveness and proving it to be a promising route to handle complex data
analysis tasks -- especially in high-dimensional datasets with high densities
of points.
