Generative quantum machine learning via denoising diffusion probabilistic models

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.

5+10 pages, 16 figures. PRL accepted version. Code available at: https://github.com/francis-hsu/quantgenmdl

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Cited by in corpus (14)

• Quantum-Noise-Driven Generative Diffusion Models
• Distributed quantum architecture search
• The role of data embedding in equivariant quantum convolutional neural networks
• Hybrid quantum-classical unsupervised data clustering based on the self-organizing feature map
• Holographic deep thermalization for secure and efficient quantum random state generation
• Permutation-equivariant quantum convolutional neural networks
• Multidimensional Quantum Generative Modeling by Quantum Hartley Transform
• Stochastic Schrödinger Equations for Quantum Reverse Diffusion
• Identification of quantum generative circuits with parallel quantum neural network
• Variational Quantum Generative Modeling by Sampling Expectation Values of Tunable Observables
• Scaling Laws of Quantum Information Lifetime in Monitored Quantum Dynamics
• Data-Driven Reconstruction and Characterization of Stochastic Dynamics via Dynamical Mode Decomposition
• Superior resilience to poisoning and amenability to unlearning in quantum machine learning
• Critical Scaling of the Quantum Wasserstein Distance