Sequences of selective rotation operators for three group clustering on qutrits by means of quantum annealing

Abstract

Recently, it was demonstrated1 that the clustering considered in this articlec, which consists in partitioning a set of data points into subsets depending on the proximity of some properties, can be performed using quantum annealing on a system of two-level quantum elements - qubits. In previous work2, we proposed to pass from qubits to qutrits - three-level quantum elements showed the advantages of such a replacement and obtained a time-dependent effective Hamiltonian. In the present paper, we have found a sequence of selective rotation operators that allows one to realize adiabatic evolution with this effective Hamiltonian in the discrete-time approximation. On five qutrits, represented by spins S = 1, we performed a simulation of clustering a set of six points on a plane into three groups by means of quantum annealing.