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.
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