Structured Models for Quantum Generative Learning

Quantum generative learning offers immense potential as the natural machine learning application of quantum computers, but it faces several trainability challenges. However, certain restricted and structured quantum generative models have a potential to overcome these trainability issues, while allowing the efficient classical estimation of the expectation values and gradients of local observables. These estimates can be used to train the quantum model completely classically, thus also eliminating the need for quantum gradient computation. Furthermore, some classes of quantum models, such as IQP or matchgate circuits, enable this type of classical training, while requiring a quantum device for efficient sampling. In this work, we study such restricted and structured quantum generative models that maintain classical trainability while having a potential for quantum advantage in sampling.