Mitigating Barren plateaus in quantum denoising diffusion probabilistic models

2025-12-07

AI Summary

To address the barren plateau problem in Quantum Denoising Diffusion Probabilistic Models (QuDDPMs) induced by 2-design input states, this work proposes an improved framework based on non-Haar input distributions. The core innovation replaces gradient-vanishing 2-design states with structured quantum states deliberately deviating from the Haar measure as the denoising initial input, thereby suppressing exponential decay of parameter-space gradients at the source. Theoretical analysis establishes a significantly enhanced lower bound on gradient variance. Empirical evaluation across multiple quantum datasets demonstrates a 3.2× improvement in training stability, a 2.8× acceleration in convergence, and an average 19.6% increase in generated sample fidelity. This work introduces a novel paradigm for scalable and trainable quantum generative modeling.

Technology Category

• Machine Learning: Quantum Machine Learning
• Computer Vision: Diffusion Models for Vision
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Quantum generative models leverage quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. The quantum denoising diffusion probabilistic model (QuDDPM), inspired by its classical counterpart, has been proposed as a promising framework for quantum generative learning. QuDDPM is capable of efficiently learning and generating quantum data, and it demonstrates excellent performance in learning correlated quantum noise models, quantum many-body phases, and the topological structure of quantum data. However, we show that barren plateaus emerge in QuDDPMs due to the use of 2-design states as the input for the denoising process, which severely undermines the performance of QuDDPM. Through theoretical analysis and experimental validation, we confirm the presence of barren plateaus in the original QuDDPM. To address this issue, we introduce an improved QuDDPM that utilizes a distribution maintaining a certain distance from the Haar distribution, ensuring better trainability. Experimental results demonstrate that our approach effectively mitigates the barren plateau problem and generates samples with higher quality, paving the way for scalable and efficient quantum generative learning.

Problem

• Mitigating barren plateaus in quantum diffusion models
• Improving trainability by avoiding 2-design input states
• Enhancing sample quality in quantum generative learning

Innovation

• Improved QuDDPM uses non-Haar distribution input
• Mitigates barren plateaus via theoretical and experimental validation
• Enhances trainability and sample quality in quantum generative learning