Quantum State Generation with Structure-Preserving Diffusion Model
Yuchen Zhu Tianrong Chen Evangelos A. Theodorou Xie Chen Molei Tao
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.