Quantum generative learning via diffusion

Deep generative models are key-enabling technology to computer vision, text generation, and large language models. Generative models for quantum data offer a promising route toward learning and preparing complex quantum-state ensembles. In this talk, I will introduce the quantum denoising diffusion probabilistic model (QuDDPM) [1], which adapts the diffusion-model idea to quantum systems through a forward randomization process and a trainable backward denoising dynamics. I will discuss how this framework enables stepwise learning of target quantum state ensembles and demonstrate its capabilities in various learning tasks. I will then present its extension to mixed states to eliminate the need for scrambling [2]. I will conclude with a brief discussion of recent results on scaling laws of quantum information lifetime in monitored quantum dynamics, emphasizing how mid-circuit measurements can maintain information and provide useful intuition for measurement-assisted quantum machine learning.