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Generative modeling has seen a rising interest in both classical and quantummachine learning, and it represents a promising candidate to obtain a practicalquantum advantage in the near term. In this study, we build over a proposedframework for evaluating the generalization performance of generative models,and we establish the first quantitative comparative race towards practicalquantum advantage (PQA) between classical and quantum generative models, namelyQuantum Circuit Born Machines (QCBMs), Transformers (TFs), Recurrent NeuralNetworks (RNNs), Variational Autoencoders (VAEs), and Wasserstein GenerativeAdversarial Networks (WGANs). After defining four types of PQAs scenarios, wefocus on what we refer to as potential PQA, aiming to compare quantum modelswith the best-known classical algorithms for the task at hand. We let themodels 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 inthe data-limited regime than the other state-of-the-art classical generativemodels. Such a feature is highly desirable in a wide range of real-worldapplications where the available data is scarce.

A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models