Nontrivial solitonic attractors of nonlinear quantum equations: Application to associative memory

Nowadays a lot of studies are devoted to non-Von Neumann architectures for information processing to achieve brain-like (neuromorphic) functionality for some tasks. On the other hand, there is an explosion of interest to quantum information processing systems and a lot of institutions and companies recently realized NISQ era devices. Thus, it is of great interest whether neuromorphic computing can be combined with quantum approaches. One of the fundamental concepts in neuromorphic computation are associative memories which can be considered as a dissipative dynamical system where attractors represent stored patterns. Recently, it was shown [V.V. Cherny, T. Byrnes, A.N. Pyrkov, Adv. Quantum Technol. 2, 1800087 (2019); A.N. Pyrkov, T. Byrnes, V.V. Cherny, arxiv: 1909.05082] that the nonlinear Schrodinger equation with a simplified dissipative perturbation of special kind and the complex Ginzburg-Landau equation feature a zero-velocity solitonic solution of non-zero amplitude which can be used in analogy to attractors of Hopfield's associative memory. This kind of solitonic attractors can be realized in Bose-Einstein condensates and nonlinear optical systems. Here we give brief summary of the works and present some new data for the approach.