Clustering into Three Groups on a Quantum Processor of Five Spins S = 1, Controlled by Pulses of Resonant RF Fields

We consider a quantum processor based on five qutrits represented by spins S = 1, which is driven by radio frequency (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 evolution intervals in the control pulse sequence, which made it possible to engineer a time-dependent effective Hamiltonian in the discrete-time approximation. Also we studied the dependence of the implementation fidelity on the parameters. We took quadrupole nuclei as qutrits, but the results obtained will be useful for controlling quantum processors based on qutrits represented by other systems.