Organizations: Jülich Supercomputing Centre, Forschungszentrum Jülich, Jülich, Germany · University of Iceland, Reykjav´ık, Iceland · RWTH Aachen University, Aachen, Germany · University of Cologne, Cologne, Germany
Abstract
Statistical downscaling is a crucial component of the weather modeling field, where high-resolution outputs must be reconstructed from coarse-resolution inputs with the full cost of dynamical refinement. In this work, we investigate a hybrid quantum-classical corrective diffusion model for probabilistic statistical downscaling of weather fields. The proposed model inserts variational quantum circuit layers into the most compressed bottleneck of the diffusion UNet while leaving the regression branch fully classical. This placement tests whether quantum circuits can act as compact nonlinear feature maps for latent-channel mixing. We evaluate intra-channel and cross-channel ansätze on 10m wind components. On the 2020 validation set, the hybrid models remain stable, preserve the large-scale spatial organization of the generated wind fields, and improve both MAE and CRPS relative to a classical corrective diffusion model in several configurations. Structural diagnostics further show that the hybrid variants preserve kinetic-energy spectra and windspeed distributions similar to its classical counterpart while producing controlled changes in tail behavior, extreme-windspeed localization, and joint wind field components structure. Backend studies on the 2020 validation set show negligible impact from simulated device noise at the tested circuit scale, whereas real-hardware deployment remains limited by qubit availability and execution fidelity. The 2021 out-of-distribution test shows that these in-distribution gains do not transfer uniformly under temporal shift, revealing a generalization gap that motivates future mitigation through stabilization and regularization. These results show that bottleneck-level quantum hybridization can make a nontrivial contribution to weather statistical downscaling, while also highlighting that circuit scale and hardware deployment remain key limiting factors.
Quantum diffusion models provide a physics-consistent route to generative learning by formulating noising and denoising directly on quantum states. However, applying such models to classical high-dimensional data is constrained by the qubit cost of state encoding and the computational burden of simulating large density operators. We propose a scalable hybrid generative pipeline that combines a classical autoencoder for dimensionality reduction with a mixed-state quantum denoising diffusion probabilistic model (MSQuDDPM) operating in the learned latent space. The autoencoder compresses data into compact latent codes that can be embedded into a small-qubit Hilbert space, after which the quantum diffusion model learns a generative distribution over latent density operators and decodes samples back to the original domain. Algorithmically, we simplify the reverse dynamics by predicting an estimate of the clean state ρ0 at timestep t and computing the one-step reverse update via an analytic backward propagation rule, rather than learning an explicit predictor for ρt−1. We demonstrate the proposed approach on MNIST image generation and discuss how mixed-state quantum diffusion can serve as a practical backbone for hybrid quantum--classical generative modeling under realistic qubit budgets.
Time series forecasting largely benefits from combining the strengths of different models, especially using a scheme where a model corrects another model by capturing supplementary patterns from forecasting errors. Concurrently, quantum models are providing a means to augment the classical capacity, including in time series forecasting, by acting alongside classical models in hybrid architectures. In this work, we propose the first forecasting system based on error correction that jointly uses quantum and classical models. Here, quantum models first extract patterns by exploring quantum phenomena, and classical models capture the remaining patterns from the quantum errors. Compared to classical single models and classical-classical hybrid models based on error correction, the complementary capacity that emerges from this quantum-classical system provided the best results in most of the addressed problems. Therefore, this work paves the way to introduce quantum models in established hybridization schemes for time series forecasting.
Jonathan H. A. de Carvalho, Filipe C. de L. Duarte, Fernando M. de Paula Neto +1
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× 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←πtanh(⋅), 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.