  Boltzmann Machines constitute a class of neural networks with applications to
image reconstruction, pattern classification and unsupervised learning in
general. Their most common variants, called Restricted Boltzmann Machines
(RBMs) exhibit a good trade-off between computability on existing silicon-based
hardware and generality of possible applications.
  Still, the diffusion of RBMs is quite limited, since their training process
proves to be hard. The advent of commercial Adiabatic Quantum Computers (AQCs)
raised the expectation that the implementations of RBMs on such quantum devices
could increase the training speed with respect to conventional hardware. To
date, however, the implementation of RBM networks on AQCs has been limited by
the low qubit connectivity when each qubit acts as a node of the neural
network.
  Here we demonstrate the feasibility of a complete RBM on AQCs, thanks to an
embedding that associates its nodes to virtual qubits, thus outperforming
previous implementations based on incomplete graphs.
  Moreover, to accelerate the learning, we implement a semantic quantum search
which, contrary to previous proposals, takes the input data as initial boundary
conditions to start each learning step of the RBM, thanks to a reverse
annealing schedule. Such an approach, unlike the more conventional forward
annealing schedule, allows sampling configurations in a meaningful neighborhood
of the training data, mimicking the behavior of the classical Gibbs sampling
algorithm.
  We show that the learning based on reverse annealing quickly raises the
sampling probability of a meaningful subset of the set of the configurations.
Even without a proper optimization of the annealing schedule, the RBM
semantically trained by reverse annealing achieves better scores on
reconstruction tasks.
