  We study the case where quantum computing could improve jet clustering by
considering two new quantum algorithms that might speed up classical jet
clustering algorithms. The first one is a quantum subroutine to compute a
Minkowski-based distance between two data points, while the second one consists
of a quantum circuit to track the rough maximum into a list of unsorted data.
When one or both algorithms are implemented in 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. Furthermore,
in the first two algorithms, an exponential speed up in dimensionality and data
length can be achieved when applying the distance or the maximum search
algorithm. In the $k_T$ algorithm, a quantum version of the same order as
FastJet is achieved.
