  We propose a novel quantum model for the restricted Boltzmann machine (RBM),
in which the visible units remain classical whereas the hidden units are
quantized as noninteracting fermions. The free motion of the fermions is
parametrically coupled to the classical signal of the visible units. This model
possesses a quantum behaviour such as coherences between the hidden units.
Numerical experiments show that this fact makes it more powerful than the
classical RBM with the same number of hidden units. At the same time, a
significant advantage of the proposed model over the other approaches to the
Quantum Boltzmann Machine (QBM) is that it is exactly solvable and efficiently
trainable on a classical computer: there is a closed expression for the
log-likelihood gradient with respect to its parameters. This fact makes it
interesting not only as a model of a hypothetical quantum simulator, but also
as a quantum-inspired classical machine-learning algorithm.
