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 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 \emph{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 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.

翻译：深度生成模型是计算机视觉、文本生成和大语言模型的关键使能技术。去噪扩散概率模型（DDPMs）近期因在诸多计算机视觉任务中生成多样化高质量样本的能力、灵活模型架构的兼容性及相对简单的训练方案而备受关注。受量子纠缠与叠加特性赋能的量子生成模型，为学习经典与量子数据提供了全新视角。受经典对应模型启发，我们提出"量子去噪扩散概率模型"（QuDDPM），以实现量子数据的高效可训练生成式学习。QuDDPM采用足够深度的电路层保证表达能力，同时引入多个中间训练任务作为目标分布与噪声之间的插值，从而避免贫瘠高原现象并确保高效训练。我们给出了学习误差的界，并展示了QuDDPM在学习相关量子噪声模型、量子多体相及量子数据拓扑结构方面的能力。这些结果为构建通用且高效的量子生成式学习提供了范式。