This article considers the generative modeling of the (mixed) states of quantum systems, and an approach based on denoising diffusion model is proposed. The key contribution is an algorithmic innovation that respects the physical nature of quantum states. More precisely, the commonly used density matrix representation of mixed-state has to be complex-valued Hermitian, positive semi-definite, and trace one. Generic diffusion models, or other generative methods, may not be able to generate data that strictly satisfy these structural constraints, even if all training data do. To develop a machine learning algorithm that has physics hard-wired in, we leverage mirror diffusion and borrow the physical notion of von Neumann entropy to design a new map, for enabling strict structure-preserving generation. Both unconditional generation and conditional generation via classifier-free guidance are experimentally demonstrated efficacious, the latter enabling the design of new quantum states when generated on unseen labels.

翻译：本文研究量子系统（混合）态的生成建模，并提出一种基于去噪扩散模型的方法。核心贡献在于一种尊重量子态物理本质的算法创新。具体而言，混合态常用的密度矩阵表示需满足复值厄米性、半正定性与迹为一的条件。通用扩散模型或其他生成方法可能无法生成严格满足这些结构约束的数据，即使所有训练数据均满足。为开发一种内置物理约束的机器学习算法，我们利用镜像扩散技术，并借鉴冯·诺依曼熵的物理概念设计新型映射，以实现严格的结构保持生成。实验证明无条件生成与基于分类器自由引导的条件生成均具实效性，后者在未见标签上生成时能够实现新型量子态的设计。