Learning Quantum Distributions with Variational Diffusion Models

It is challenging to identify the state of many-body quantum systems, as recovering density matrices underlying the quantum state typically requires computational resources scale exponentially to the system size. In this work, we introduce the variational diffusion model (VDM) to efficiently learn high-dimensional quantum distributions with high fidelity, which is essential to realize the fast reconstruction of quantum states. We build up the VDM suitable for dealing with the high-dimensional quantum samples, and then perform numerical experiments to test our model and other autoregressive models, including recurrent neural network and transformer. It is found that the VDM can achieve a modest better performance with fewest parameters than other two to learn the distribution as desired. Our results pave the way to applying diffusion models to solve hard problems in the quantum domain.