  Deep generative models are key-enabling technology to computer vision, text
generation, and large language models. Denoising diffusion probabilistic models
(DDPMs) have recently gained much attention due to their ability to generate
diverse and high-quality samples in many computer vision tasks, as well as to
incorporate flexible model architectures and a relatively simple training
scheme. Quantum generative models, empowered by entanglement and superposition,
have brought new insight to learning classical and quantum data. Inspired by
the classical counterpart, we propose the quantum denoising diffusion
probabilistic model (QuDDPM) to enable efficiently trainable generative
learning of quantum data. QuDDPM adopts sufficient layers of circuits to
guarantee expressivity, while it introduces multiple intermediate training
tasks as interpolation between the target distribution and noise to avoid
barren plateau and guarantee efficient training. We provide bounds on the
learning error and demonstrate QuDDPM's capability in learning correlated
quantum noise model, quantum many-body phases, and topological structure of
quantum data. The results provide a paradigm for versatile and efficient
quantum generative learning.
