Zhang Bingzhi, Xu Peng, Chen Xiaohui, Zhuang Quntao
Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA.
Ming Hsieh Department of Electrical and Computer Engineering, University of Southern California, Los Angeles, California 90089, USA.
Phys Rev Lett. 2024 Mar 8;132(10):100602. doi: 10.1103/PhysRevLett.132.100602.
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.
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支撑技术。去噪扩散概率模型（DDPMs）最近备受关注，因为它们能够在许多计算机视觉任务中生成多样且高质量的样本，还能融入灵活的模型架构和相对简单的训练方案。受纠缠和叠加赋能的量子生成模型，为经典数据和量子数据的学习带来了新的见解。受经典对应模型的启发，我们提出了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来保证表达能力，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，以避免贫瘠高原并保证高效训练。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、量子多体相以及量子数据的拓扑结构方面的能力。这些结果为通用且高效的量子生成学习提供了一个范例。
