Holographic implementation of quantum-like cognitive models

Subject of study. A 4 f Fourier-holography scheme with phase conjugation in the correlation plane and the corresponding Grossberg “Instar” neural-network model were examined to assess the feasibility of implementing quantum-like models of information processing. Aim of study. The aim was to develop a Fourier-holography scheme model consistent with the mathematical formalism of quantum mechanics used in quantum-like cognitive models. Method. Analytical modeling and numerical simulations were performed by representing the processed information with a homogeneous isotropic random field model. Main results. The results showed that the Fourier-holography setup incorporating nonlinear phase conjugation in the correlation plane could serve as a limited analog of a quantum system in terms of parallel processing and choice from a superposition. In this case, the choice was not random; rather, it was determined by the nonlinear transfer function of the phase-conjugating mirror. The shift-invariance, ensured by a thin Fourier hologram, imparted an additional capability—making decisions in the form of a superposition described by a linear prediction model; some researchers consider this approach as a possible mechanism underlying the phenomenon of intuition. Practical significance. An analytical description, consistent with the information-processing model, is required for developing holographic simulators of quantum information-processing systems and computing devices.