Universality of Many-body Projected Ensemble for Learning Quantum Data Distribution

Recent advancements highlight the pivotal role of quantum machine learning (QML) [4, 13] in processing quantum data derived from quantum systems [14]. A fundamental task in QML is generating quantum data by learning the underlying distribution, essential for understanding quantum systems, synthesizing new samples, and advancing applications in quantum chemistry and materials science. However, extending classical generative approaches to quantum data presents significant challenges, as quantum distributions exhibit superposition, entanglement, and non-locality that classical models struggle to replicate efficiently. Quantum generative models such as quantum generative adversarial networks [24, 42] and quantum variational autoencoders [20, 38] can be used to prepare a fixed single quantum state [21, 28, 37], but are inefficient for generating ensembles of quantum states [3] due to the need for training deep parameterized quantum circuits (PQCs). The quantum denoising diffusion probabilistic model [40] offers a promising approach that employs intermediate training steps to smoothly interpolate between the target distribution and noise, thereby enabling efficient training.