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Superconducting quantum interferometers provide an opportunity to build the tunable magnetic flux transformers which are widely used as couplers in quantum circuits. Nonlinearity of Josephson junction current-phase relation allows making the transfer function of these transformers linear or vice versa highly nonlinear on demand. In this work we consider a possibility to design the flux transformers playing the role of artificial neuron and synapse of a superconducting adiabatic artificial neural network of perceptron type. Our neuron is capable of providing one-shot calculation of sigmoid and hyperbolic tangent activation functions, while synapse is featured by both positive and negative signal transfer coefficients. The proposed adiabatic artificial neural network seems to be the most energy-efficient implementation of the neuromorphic circuit of the considered type capable of operation with quantum circuits in a single cryogenic package.