Problem-informed Graphical Quantum Generative Learning*

Generative learning is a powerful paradigm in machine learning, that instead of solely discriminating between different classes, aims to understand and capture the underlying distribution of data. Quantum resources, due to their inherent probabilistic nature, can be used to efficiently draw samples from probability distributions of high complexity. This makes generative quantum machine learning (QML) a natural pathway towards harnessing the potential of quantum computing. While generative quantum models can be highly expressive, they also pose several challenges connected to their trainability. A potential way of dealing with these setbacks is by constructing problem-informed models, that can be trained more efficiently on structured problems. Probabilistic graphical models provide a universal framework for identifying structure in generative learning problems and such can be exploited to construct problem-informed QML algorithms. In this work, we propose a framework for using Markov networks in the construction of quantum circuit Born machines, that outperform previous problem-agnostic models. Furthermore, we analyze generative learning problems, that can be addressed with quantum learners based on both Bayesian and Markov networks.