  An increase in the efficiency of sampling from Boltzmann distributions would
have a significant impact on deep learning and other machine-learning
applications. Recently, quantum annealers have been proposed as a potential
candidate to speed up this task, but several limitations still bar these
state-of-the-art technologies from being used effectively. One of the main
limitations is that, while the device may indeed sample from a Boltzmann-like
distribution, quantum dynamical arguments suggest it will do so with an {\it
instance-dependent} effective temperature, different from its physical
temperature. Unless this unknown temperature can be unveiled, it might not be
possible to effectively use a quantum annealer for Boltzmann sampling. In this
work, we propose a strategy to overcome this challenge with a simple
effective-temperature estimation algorithm. We provide a systematic study
assessing the impact of the effective temperatures in the learning of a special
class of a restricted Boltzmann machine embedded on quantum hardware, which can
serve as a building block for deep-learning architectures. We also provide a
comparison to $k$-step contrastive divergence (CD-$k$) with $k$ up to 100.
Although assuming a suitable fixed effective temperature also allows us to
outperform one step contrastive divergence (CD-1), only when using an
instance-dependent effective temperature do we find a performance close to that
of CD-100 for the case studied here.

Quantum Physics