On the Expressive Power of Quantum versus Classical Generative Models

Generative models are one of the key candidates in the race for practical quantum advantage. We compare a family of quantum generative models (e.g., Quantum Circuit Born Machines) with well-known families of classical generative models (e.g., Restricted Boltzmann Machines) using several different metrics. We study the distribution of eigenvalues from the Fisher information matrix corresponding to each model and its impact on the effective dimension computed as defined in Abbas et al. Nat Comput Sci 1, 403–409 (2021). As in that study, we found that the output of the quantum generative models has a higher effective dimension than its classical counterparts, implying that the quantums model have higher expressibility and a higher capacity to generate different probability distributions.