  Generative modeling has seen a rising interest in both classical and quantum
machine learning, and it represents a promising candidate to obtain a practical
quantum advantage in the near term. In this study, we build over a proposed
framework for evaluating the generalization performance of generative models,
and we establish the first quantitative comparative race towards practical
quantum advantage (PQA) between classical and quantum generative models, namely
Quantum Circuit Born Machines (QCBMs), Transformers (TFs), Recurrent Neural
Networks (RNNs), Variational Autoencoders (VAEs), and Wasserstein Generative
Adversarial Networks (WGANs). After defining four types of PQAs scenarios, we
focus on what we refer to as potential PQA, aiming to compare quantum models
with the best-known classical algorithms for the task at hand. We let the
models race on a well-defined and application-relevant competition setting,
where we illustrate and demonstrate our framework on 20 variables (qubits)
generative modeling task. Our results suggest that QCBMs are more efficient in
the data-limited regime than the other state-of-the-art classical generative
models. Such a feature is highly desirable in a wide range of real-world
applications where the available data is scarce.
