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Artificial intelligence is rapidly developing Computer Science field, which has already taken an important place in academia and business. In particular, neural networks are of the greatest interest, since they model the work of a neuron in the human brain. In this paper, we investigate the question of constructing a physical model of a neural cell based on superconducting circuits. We have developed the design of the basic cell of the neural network the sigmoid cell (SC-neuron, see fig. 1) based on Josephson contacts without resistive shunting. The advantage of this approach is the nonlinearity of the superconducting current in the system as a function of the phase difference on the Josephson junction. In addition, superconductivity ensures high computing speed and energy efficiency of processes.