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.

翻译：深度生成模型是计算机视觉、文本生成与大语言模型的关键使能技术。去噪扩散概率模型（DDPMs）因其在众多计算机视觉任务中生成多样且高质量样本的能力，以及灵活的模型架构与相对简单的训练方案，近期备受关注。量子生成模型凭借纠缠与叠加特性，为学习经典与量子数据带来了新视角。受经典模型启发，我们提出量子去噪扩散概率模型（QuDDPM），以实现对量子数据的高效可训练生成学习。QuDDPM采用足够层数的电路以保证表达能力，同时引入多个中间训练任务作为目标分布与噪声间的插值，以避免贫瘠高原现象并确保训练效率。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、量子多体相以及量子数据拓扑结构方面的能力。该结果为通用且高效的量子生成学习提供了范式。