Associative memory on qutrits by means of quantum annealing

When associative memory is implemented on the well-studied Hopfield network, patterns are recorded in the interaction constants between binary neurons. These constants are chosen so that each pattern should have its own minimum energy of the system described by the Ising model. In the quantum version of the Hopfield network, it was proposed to recall such states by the adiabatic change of the Hamiltonian in time. Qubits, quantum elements with two states, for example, spins with S = 1/2 were considered as neurons. In this paper, for the first time, we study the function of associative memory using three-level quantum elements—qutrits, represented by spins with S = 1. We record patterns with the help of projection operators. This choice is due to the need to operate with a state with a zero spin projection, whose interaction with the magnetic field vanishes. We recall the state corresponding to one of the patterns recorded in the memory, or superposition of such states by means of quantum annealing. To equalize the probabilities of finding the system in different states of superposition, an auxiliary Hamiltonian is proposed, which is turned off at the end of evolution. Simulations were performed on two and three qutrits and an increase in the memory capacity after replacing qubits with qutrits was shown.