  Inference is the task of drawing conclusions about unobserved variables given
observations of related variables. Applications range from identifying diseases
from symptoms to classifying economic regimes from price movements.
Unfortunately, performing exact inference is intractable in general. One
alternative is variational inference, where a candidate probability
distribution is optimized to approximate the posterior distribution over
unobserved variables. For good approximations, a flexible and highly expressive
candidate distribution is desirable. In this work, we use quantum Born machines
as variational distributions over discrete variables. We apply the framework of
operator variational inference to achieve this goal. In particular, we adopt
two specific realizations: one with an adversarial objective and one based on
the kernelized Stein discrepancy. We demonstrate the approach numerically using
examples of Bayesian networks, and implement an experiment on an IBM quantum
computer. Our techniques enable efficient variational inference with
distributions beyond those that are efficiently representable on a classical
computer.
