  Although several models have been proposed towards assisting machine learning
(ML) tasks with quantum computers, a direct comparison of the expressive power
and efficiency of classical versus quantum models for datasets originating from
real-world applications is one of the key milestones towards a quantum ready
era. Here, we take a first step towards addressing this challenge by performing
a comparison of the widely used classical ML models known as restricted
Boltzmann machines (RBMs), against a recently proposed quantum model, now known
as quantum circuit Born machines (QCBMs). Both models address the same hard
tasks in unsupervised generative modeling, with QCBMs exploiting the
probabilistic nature of quantum mechanics and a candidate for near-term quantum
computers, as experimentally demonstrated in three different quantum hardware
architectures to date. To address the question of the performance of the
quantum model on real-world classical data sets, we construct scenarios from a
probabilistic version out of the well-known portfolio optimization problem in
finance, by using time-series pricing data from asset subsets of the S\&P500
stock market index. It is remarkable to find that, under the same number of
resources in terms of parameters for both classical and quantum models, the
quantum models seem to have superior performance on typical instances when
compared with the canonical training of the RBMs. Our simulations are grounded
on a hardware efficient realization of the QCBMs on ion-trap quantum computers,
by using their native gate sets, and therefore readily implementable in
near-term quantum devices.
