  Clustering is one of the most frequent problems in many domains, in
particular, in particle physics where jet reconstruction is central in
experimental analyses. Jet clustering at the CERN's Large Hadron Collider (LHC)
is computationally expensive and the difficulty of this task will increase with
the upcoming High-Luminosity LHC (HL-LHC). In this paper, we study the case in
which quantum computing algorithms might improve jet clustering by considering
two novel quantum algorithms which may speed up the classical jet clustering
algorithms. The first one is a quantum subroutine to compute a Minkowski-based
distance between two data points, whereas the second one consists of a quantum
circuit to track the maximum into a list of unsorted data. The latter algorithm
could be of value beyond particle physics, for instance in statistics. When one
or both of these algorithms are implemented into the classical versions of
well-known clustering algorithms (K-means, Affinity Propagation and $k_T$-jet)
we obtain efficiencies comparable to those of their classical counterparts.
Even more, exponential speed-up could be achieved, in the first two algorithms,
in data dimensionality and data length when the distance algorithm or the
maximum searching algorithm are applied.
