  Leveraging the intrinsic probabilistic nature of quantum systems, generative
quantum machine learning (QML) offers the potential to outperform classical
learning models. Current generative QML algorithms mostly rely on
general-purpose models that, while being very expressive, face several training
challenges. A potential way to address these setbacks involves constructing
problem-informed models capable of more efficient training on structured
problems. In particular, probabilistic graphical models provide a flexible
framework for representing structure in generative learning problems and can
thus be exploited to incorporate inductive bias in QML algorithms. In this
work, we propose a problem-informed quantum circuit Born machine Ansatz for
learning the joint probability distribution of random variables, with
independence relations efficiently represented by a Markov network (MN). We
further demonstrate the applicability of the MN framework in constructing
generative learning benchmarks and compare our model's performance to previous
designs, showing it outperforms problem-agnostic circuits. Based on a
preliminary analysis of trainability, we narrow down the class of MNs to those
exhibiting favorable trainability properties. Finally, we discuss the potential
of our model to offer quantum advantage in the context of generative learning.
