On the holographic implementation of quantum-like cognitive models

For Russian citation (Opticheskii Zhurnal):

Павлов А.В. К вопросу голографической реализации квантово-подобных моделей обработки информации // Оптический журнал. 2025. Т. 92. № 6. С. 3–13. http://doi.org/10.17586/1023-5086-2025-92-06-3-13

Pavlov A.V. On the holographic implementation of quantum-like cognitive models [in Russian] // Opticheskii Zhurnal. 2025. V. 92. № 6. P. 3–13. http://doi.org/10.17586/1023-5086-2025-92-06-3-13

For citation (Journal of Optical Technology):

Abstract:

Subject of study. 4f Fourier-holography scheme and the Grosseberg’s Instar neural network are considered in the framework of quantum-like cognitive models. Aim of study is an analytical description of the holographic scheme matched with the quantum-like models’ mathematical apparatus. Method. Analytical modeling and numerical simulation are used under representation of the processed information by realizations of a homogeneous isotropic random field. Main results. It is shown that holographic setup with nonlinear phase conjugating in the correlation plane can be some analogue of a quantum system only in terms of parallel processing and selection from super-position. However, the choice is not random, but is determined by the nonlinear transfer function of the phase-conjugating mirror. The shift invariance provided by a thin Fourier hologram adds the ability to make decision as the superposition, described by the linear prediction model; the last is considered by some authors as one of the possible mechanisms of the intuition phenomenon. Practical significance. For the classical holographic simulators of quantum processors and computers to be created their analytical description are to be matched with the used in quantum-like cognitive models’ mathematical formalism of quantum mechanics.

Keywords:

Fourier-holography, superimposed holograms, phase conjugating, density matrix, non-linearity, neural networks, quantum-like models, information processing, choice from alternatives, decision making, linear prediction

OCIS codes: 090.0090, 200.3050, 200.4260,200,4490, 070.4560

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