  Clustering is grouping of data by the proximity of some properties. We report
on the possibility of increasing the efficiency of clustering of points in a
plane using artificial quantum neural networks after the replacement of the
two-level neurons called qubits represented by the spins S = 1/2 by the
three-level neurons called qutrits represented by the spins S = 1. The problem
has been solved by the slow adiabatic change of the Hamiltonian in time. The
methods for controlling a qutrit system using projection operators have been
developed and the numerical simulation has been performed. The Hamiltonians for
two well-known cluster-ing methods, one-hot encoding and k-means ++, have been
built. The first method has been used to partition a set of six points into
three or two clusters and the second method, to partition a set of nine points
into three clusters and seven points into four clusters. The simulation has
shown that the clustering problem can be ef-fectively solved on qutrits
represented by the spins S = 1. The advantages of clustering on qutrits over
that on qubits have been demonstrated. In particular, the number of qutrits
required to represent data points is smaller than the number of qubits by a
factor of log2 N / log3 N . Since, for qutrits, it is easier to partition the
data points into three clusters rather than two ones, the approximate
hierarchical procedure of data partition-ing into a larger number of clusters
is accelerated. At the exact data partition into more than three clusters, it
has been proposed to number the clusters by the numbers of states of the
corresponding multi-spin subsys-tems, instead of using the numbers of
individual spins. This reduces even more the number of qutrits (N log3 K
instead of NK ) required to implement the algorithm.
