Generative quantum machine learning via denoising diffusion probabilistic models

TL;DR

This paper introduces QuDDPM, a quantum generative model inspired by classical diffusion models, capable of efficiently learning complex quantum data and structures through layered circuits and intermediate training tasks.

Contribution

It proposes the quantum denoising diffusion probabilistic model (QuDDPM), combining classical diffusion techniques with quantum circuit expressivity and training strategies.

Findings

Successfully learns correlated quantum noise models

Capable of identifying quantum many-body phases

Detects topological structures in quantum data

Abstract

Deep generative models are key-enabling technology to computer vision, text generation, and large language models. Denoising diffusion probabilistic models (DDPMs) have recently gained much attention due to their ability to generate diverse and high-quality samples in many computer vision tasks, as well as to incorporate flexible model architectures and a relatively simple training scheme. Quantum generative models, empowered by entanglement and superposition, have brought new insight to learning classical and quantum data. Inspired by the classical counterpart, we propose the quantum denoising diffusion probabilistic model (QuDDPM) to enable efficiently trainable generative learning of quantum data. QuDDPM adopts sufficient layers of circuits to guarantee expressivity, while it introduces multiple intermediate training tasks as interpolation between the target distribution and noise to avoid barren plateau and guarantee efficient training. We provide bounds on the learning error and demonstrate QuDDPM's capability in learning correlated quantum noise model, quantum many-body phases, and topological structure of quantum data. The results provide a paradigm for versatile and efficient quantum generative learning.