Quantum Circuits in Diffusion Models: A Fair-Comparison Study and a Mechanistic Analysis of Angle-Embedding Failures
2026-07-10 • Machine Learning
Machine Learning
AI summaryⓘ
The authors explore adding small quantum circuits into diffusion models used for generating images, isolating the quantum parts to see their effect. They compare quantum circuits with classical ones on datasets like MNIST and CIFAR-10 and find that quantum versions perform about as well but do not show a clear advantage in efficiency when parameters are matched. They also discover a technical issue in one model type caused by how quantum inputs are encoded, which they fix with a bounding function that improves performance. The work is done through classical simulation and focuses on fair comparison rather than claiming quantum advantage.
variational quantum circuitsdiffusion modelssqueeze-and-excitationDDPMlatent diffusionscore-based modelsangle embeddingphase aliasingFID (Fréchet Inception Distance)quantum parameter efficiency
Authors
Jaeuk Kim, Sanghoon Yoo
Abstract
We study the integration of variational quantum circuits (VQCs) into diffusion models through a squeeze-and-excitation (SE) channel-modulation scaffold that isolates the quantum contribution. Using a role-matched classical control and multi-seed significance testing across DDPM and latent diffusion on MNIST and CIFAR-10, with a score-based NCSN study on MNIST, we find that quantum cores achieve comparable mean FID to the classical control across DDPM and latent diffusion, while paired sampling-seed tests for EfficientSU2 detect no statistically significant difference. Although the quantum cores use $4.5$--$9\times$ fewer core parameters than the role-matched control, parameter-matched classical controls attain comparable mean FID, so the experiments do not establish a quantum parameter-efficiency advantage. We further identify a structural failure in score-based NCSN: the unbounded score target, proportional to $1/σ$, drives angle-embedding inputs far beyond the $2π$ period of rotation gates, causing phase aliasing and collapse of the quantum modulator. A bounding transformation, $θ\leftarrow π\tanh(\cdot)$, maps inputs to the non-aliasing domain and substantially improves both quantum cores. Since all circuits are classically simulated at a few-qubit scale, we do not claim quantum advantage. Instead, the study provides a fair-comparison protocol for quantum-enhanced generative models and a mechanistic account of when and why angle embeddings fail.