Quantum Circuits in Diffusion Models A Fair Comparison Study and a Mechanistic Analysis of Angle Embedding Failures

Jul 16, 2026

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Integration of variational quantum circuits (VQCs) into diffusion models is studied using a squeeze-and-excitation (SE) channel-modulation scaffold that isolates the quantum contribution. Role-matched classical control and multi-seed significance testing across DDPM and latent diffusion on MNIST and CIFAR-10 show comparable mean FID, with paired tests finding no statistically significant difference. Although quantum cores use fewer parameters, matched-budget comparisons yield only small, non-significant gains. Mechanistic analysis attributes failures in score-based NCSN to angle-embedding aliasing from unbounded 1/σ targets, fixed by bounding θ via π tanh, improving FID and showing inductive-bias parity rather than quantum advantage.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

Abstract

Introduction

Contributions

arXiv :2607 .09 108v 1 [ cs .LG] 10 Jul 2026 Quantum Circuits in Diffusion Models: A Fair-Comparison Study and a Mechanistic Analysis of Angle-Embedding Failures Jaeuk Kim Sanghoon Yoo NextITS Co. , Ltd. [freak91uk@hnextits.com](freak91uk@hnextits.com) , [stmlshu@hnextits.com](stmlshu@hnextits.com) 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 (a classical MLP that plays the identical role in the same scaffold) and multi-seed significance testing across DDPM and latent diffusion on MNIST and CIFAR-10 (with a score-based NCSN study on MNIST), both quantum cores achieve comparable mean FID to the role-matched classical control across DDPM and latent diffusion, while paired sampling-seed tests for EfficientSU2 detect no statistically significant difference. While the quantum cores use 4.5–9 × fewer parameters than this control, at matched budgets they attain slightly lower mean FID in all four MNIST/CIFAR-10 comparisons; the differences are small and not significance-tested, so the experiments do not establish a quantum parameter-efficiency advantage. We further mechanistically identify and resolve a structural failure in the score-based NCSN setting: the unbounded score target (∝ 1/σ) drives angleembedding inputs far beyond the 2π period of the rotation gates, a phase-aliasing effect that flattens the expectation-value landscape and collapses the quantum modulator. A bounding transformation θ ← π tanh(·) projects the feature space onto the non-aliasing domain (−π, π), removing the failure and substantially improving both quantum cores; normalized RealAmplitudes attains the lowest mean FID in this single-training-run comparison (not established as statistically significant) . Because all circuits are classically simulated at a few-qubit scale, we characterize whether a variational quantum parameterization is a useful inductive bias under strictly matched controls, rather than claiming quantum advantage; under this controlled comparison the quantum core exhibits functional parity—not superiority—with a classical core of equal parameter budget. Our contributions are (i) a rigorous fair-comparison methodology for quantum-enhanced generative models and (ii) a mechanistic account of when and why angle embeddings fail. 1 Introduction Quantum machine learning (QML) [4] for generative modeling has attracted strong interest, with a growing body of work inserting parameterized quantum circuits into autoencoders, GANs, and, more recently, diffusion models [14, 22] . A recurring difficulty in this literature is evaluation: a quantum-augmented model is often compared against a plain baseline without a classical module of matched capacity in the same location, so an observed gain may simply reflect the extra parameters and nonlinearity of the inserted block rather than anything quantum. When the quantum circuit is small enough to be classically simulable, as is the case at the few-qubit scale used in practice, the experiments are not designed to test computational quantum advantage; what remains to be measured is whether the quantum parameterization is a useful inductive bias relative to a classical core playing the same role. We therefore adopt a deliberately conservative experimental design. We fix a single squeezeand-excitation (SE) modulation scaffold and vary only its core, swapping a variational quantum circuit for a role-matched classical multilayer perceptron (MLP)—one that occupies the identical position in the same scaffold, though with more core parameters (144 vs. 16/32), making it a higher-parameter, not smaller, control—or for nothing at all, with all wrappers, initializations, and training schedules held identical. Differences are then assessed with multi-seed significance testing rather than single-run point estimates

FAQs

How does the study ensure a fair comparison between quantum and classical diffusion models?

It fixes a shared squeeze-and-excitation (SE) modulation scaffold and swaps only the core between a variational quantum circuit, a role-matched classical MLP in the same position, or nothing, while keeping initialization and training schedules identical, then uses multi-seed significance testing.

Do quantum cores provide a statistically significant generative-quality advantage in DDPM or latent diffusion?

No. Across DDPM and latent diffusion on MNIST/CIFAR-10, quantum cores match the higher-parameter classical control in mean FID, and paired sampling-seed tests detect no statistically significant difference.

What mechanistic reason explains angle-embedding failures in score-based NCSN models?

The unbounded score target scales with 1/σ, pushing angle-embedding inputs beyond the 2π period of rotation gates, causing phase aliasing that flattens the expectation-value landscape and collapses the quantum modulator.

Jul 16, 2026

Upload by Skyler