Clustering into three groups on a quantum processor of five spins S = 1, controlled by pulses of resonant RF fields

Abstract

We consider a quantum processor based on five qutrits represented by spins S=1, which is driven by radio fre-quency (RF) pulses selective in transitions between adjacent levels. Numerical simulation of the implementation of the quantum-adiabatic clustering algorithm was performed on the example of partitioning a set of six points into three groups. We find the amplitudes and durations of rectangular RF pulses, as well as the durations of free evolu-tion intervals in the control pulse sequence, which made it possible to engineer a time-dependent effective Hamilto-nian in the discrete-time approximation. Also we studied the dependence of the implementation fidelity on the pa-rameters. We took quadrupole nuclei as qutrits, but the results obtained will be useful for controlling quantum pro-cessors based on qutrits represented by other systems.