Alignment of the amplitudes of stored states for solving the associative memory problem using quantum annealing
The solution of combinatorial optimization problems by means of quantum annealing is based on the preparation of an equally superposition state. Such superposition is crucial to the associative memory problem of correctly recalling patterns. In this paper, we study the alignment of the amplitudes of stored states in memory using the proposed auxiliary Hamiltonian, which is switched off at the end of evolution. The results of the algorithm execution were obtained both by numerical modeling and by the perturbation theory method, which made it possible to obtain the dependences on physical parameters in explicit form. As examples, systems of two and three qutrits, represented by spins S=1, are considered. Since the Hamiltonian is expressed in a univer-sal form through projectors onto states stored in memory, it can be used for other quantum sys-tems (platforms).