  We consider a model of an artificial neural network that uses
quantum-mechanical particles in a two-humped potential as a neuron. To simulate
such a quantum-mechanical system the Monte-Carlo integration method is used. A
form of the self-potential of a particle and two potentials (exciting and
inhibiting) interaction are proposed. The possibility of implementing the
simplest logical elements, (such as AND, OR and NOT) based on introduced
quantum particles is shown. Further we show implementation of a simplest
convolutional network. Finally we construct a network that recognizes
handwritten symbols, which shows that in the case of simple architectures, it
is possible to transfer weights from a classical network to a quantum one.
