  A successful application of quantum annealing to machine learning is training
restricted Boltzmann machines (RBM). However, many neural networks for vision
applications are feedforward structures, such as multilayer perceptrons (MLP).
Backpropagation is currently the most effective technique to train MLPs for
supervised learning. This paper aims to be forward-looking by exploring the
training of MLPs using quantum annealers. We exploit an equivalence between
MLPs and energy-based models (EBM), which are a variation of RBMs with a
maximum conditional likelihood objective. This leads to a strategy to train
MLPs with quantum annealers as a sampling engine. We prove our setup for MLPs
with sigmoid activation functions and one hidden layer, and demonstrated
training of binary image classifiers on small subsets of the MNIST and
Fashion-MNIST datasets using the D-Wave quantum annealer. Although problem
sizes that are feasible on current annealers are limited, we obtained
comprehensive results on feasible instances that validate our ideas. Our work
establishes the potential of quantum computing for training MLPs.
