Mitigating Barren Plateaus in Quantum Denoising Diffusion Probabilistic Model

TL;DR

This paper addresses the scalability challenge of quantum denoising diffusion models by identifying barren plateau issues and proposing architectural improvements and a conditional model to enhance trainability and utility.

Contribution

It provides a theoretical and experimental analysis of barren plateaus in QuDDPM and introduces methods to mitigate this problem, enabling larger-scale quantum generative modeling.

Findings

Identified the origin of barren plateaus in QuDDPM.

Proposed architectural enhancements to mitigate barren plateaus.

Demonstrated improved trainability and scalability of quantum diffusion models.

Abstract

Quantum generative models exploit quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. Recently, inspired by classical diffusion frameworks, the quantum denoising diffusion probabilistic model (QuDDPM) has emerged as a powerful tool for learning correlated noise models, many-body phases, and topological data structure. However, we demonstrate that QuDDPM's efficacy is currently restricted to small-scale systems (typically $\le$ 5 qubits). As the system size increases, a severe barren plateau (BP) problem emerges, fundamentally limiting the model's scalability. We provide rigorous theoretical proofs and experimental validation to identify the origin of this BP, distinct from previously known causes. To restore trainability, we introduce an architectureal enhancement that mitigates the BP and ensures training stability. Furthermore, we propose a conditional QuDDPM, capable of generating ground states based on Hamiltonian parameters, significantly expanding the utility of quantum generative models for complex quantum state preparation. Our approach not only restores the scalability and trainability bottlenecks of quantum diffusion models but also provides a robust tool for exploring complex quantum matter and state preparation in the NISQ era.