  Quantum annealing (QA) is a hardware-based heuristic optimization and
sampling method applicable to discrete undirected graphical models. While
similar to simulated annealing, QA relies on quantum, rather than thermal,
effects to explore complex search spaces. For many classes of problems, QA is
known to offer computational advantages over simulated annealing. Here we
report on the ability of recent QA hardware to accelerate training of fully
visible Boltzmann machines. We characterize the sampling distribution of QA
hardware, and show that in many cases, the quantum distributions differ
significantly from classical Boltzmann distributions. In spite of this
difference, training (which seeks to match data and model statistics) using
standard classical gradient updates is still effective. We investigate the use
of QA for seeding Markov chains as an alternative to contrastive divergence
(CD) and persistent contrastive divergence (PCD). Using $k=50$ Gibbs steps, we
show that for problems with high-energy barriers between modes, QA-based seeds
can improve upon chains with CD and PCD initializations. For these hard
problems, QA gradient estimates are more accurate, and allow for faster
learning. Furthermore, and interestingly, even the case of raw QA samples (that
is, $k=0$) achieved similar improvements. We argue that this relates to the
fact that we are training a quantum rather than classical Boltzmann
distribution in this case. The learned parameters give rise to hardware QA
distributions closely approximating classical Boltzmann distributions that are
hard to train with CD/PCD.
