This article considers the generative modeling of the 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 the recent
development of Mirror Diffusion Model and design a previously unconsidered
mirror map, to enable strict structure-preserving generation. Both
unconditional generation and conditional generation via classifier-free
guidance are experimentally demonstrated efficacious, the latter even enabling
the design of new quantum states when generated on unseen labels.

针对量子系统状态的生成建模问题，本文提出了一种基于去噪扩散模型的方法，其关键创新点在于考虑了物理性质中的量子状态约束，通过 Mirror Diffusion Model 和设计出的镜像映射实现了严格保持结构的生成，实验验证了无条件生成和通过无监督分类器引导的条件生成的有效性，后者甚至在未知标签上生成了新的量子状态。