Abstract The major computational bottleneck of operational Numerical Weather Prediction (NWP) is data assimilation, in which a high-dimensional, prohibitively expensive variational cost function must be minimised repeatedly, with computational costs scaling alongside model resolution. This work presents a systematic empirical evaluation of an Adaptive Hybrid Variational Quantum-Classical (VQE)-based framework for Four-Dimensional Variational Data Assimilation (4DVAR), benchmarked against Classical BFGS optimisation and three deep learning baselines: a standard Long Short-Term Memory network (LSTM), a task-aligned Data Assimilation LSTM (DA-LSTM), and a Neural Ordinary Differential Equation (Neural ODE) across two canonical chaotic atmospheric models of increasing complexity: the three-variable Lorenz-1963 (L63) and the forty-variable Lorenz-1996 (L96) systems. All experiments were conducted using PennyLane quantum simulation across 50 independent runs per method, with rigorous statistical validation including paired t-tests, Wilcoxon signed-rank tests, bootstrap 95% confidence intervals, and formal effect size estimation. Results are reported with full timing decomposition separating quantum circuit execution (T 1 ), classical optimiser time (T 2 ), and infrastructure overhead (T 3 ). The central finding is that the Adaptive Hybrid Quantum-Classical model with a Hardware-Efficient Ansatz (Hybrid QC-HEA) achieves a mean 4DVAR cost of 2.10 on L63 and 21.0 on L96 representing only 11.7% and 14.8% above the Classical 4DVAR baseline respectively—differences that are not statistically significant at p < 0.05. Crucially, Hybrid QC-HEA outperforms all three deep learning baselines by substantial margins on L96, achieving 5.5x lower cost than DA-LSTM, 5.2x lower than LSTM, and 8.3x lower than Neural ODE. The Hybrid QC-HEA also exhibits the tightest cost distribution across 50 runs on L96, demonstrating superior operational reliability compared to all competing methods. Conversely, all-quantum VQE-based methods with no refinement by classical methods scale to cost 32 and 75x more than classical on L96, and thus gradient-free quantum optimisation without the classical BFGS refinement step is ultimately impractical to high-precision data assimilation and the classical BFGS refinement step is in any case a fundamental element of the architecture. Computational scaling analysis reveals that Classical 4DVAR wall-clock time grows 126-fold from L63 to L96, consistent with theoretical predictions of exponentially increasing complexity in chaotic optimisation landscapes, while the hybrid framework maintains near-classical accuracy at both scales. These results constitute an empirical proof-of-concept for hybrid quantum-classical data assimilation on realistic atmospheric models, establishing a reproducible benchmarking framework for future investigation on near-term quantum processors based NISQ devices.
Abstract The major computational bottleneck of operational Numerical Weather Prediction (NWP) is data assimilation, in which a high-dimensional, prohibitively expensive variational cost function must be minimised repeatedly, with computational costs scaling alongside model resolution. This work presents a systematic empirical evaluation of an Adaptive Hybrid Variational Quantum-Classical (VQE)-based framework for Four-Dimensional Variational Data Assimilation (4DVAR), benchmarked against Classical BFGS optimisation and three deep learning baselines: a standard Long Short-Term Memory network (LSTM), a task-aligned Data Assimilation LSTM (DA-LSTM), and a Neural Ordinary Differential Equation (Neural ODE) across two canonical chaotic atmospheric models of increasing complexity: the three-variable Lorenz-1963 (L63) and the forty-variable Lorenz-1996 (L96) systems. All experiments were conducted using PennyLane quantum simulation across 50 independent runs per method, with rigorous statistical validation including paired t-tests, Wilcoxon signed-rank tests, bootstrap 95% confidence intervals, and formal effect size estimation. Results are reported with full timing decomposition separating quantum circuit execution (T 1 ), classical optimiser time (T 2 ), and infrastructure overhead (T 3 ). The central finding is that the Adaptive Hybrid Quantum-Classical model with a Hardware-Efficient Ansatz (Hybrid QC-HEA) achieves a mean 4DVAR cost of 2.10 on L63 and 21.0 on L96 representing only 11.7% and 14.8% above the Classical 4DVAR baseline respectively—differences that are not statistically significant at p < 0.05. Crucially, Hybrid QC-HEA outperforms all three deep learning baselines by substantial margins on L96, achieving 5.5x lower cost than DA-LSTM, 5.2x lower than LSTM, and 8.3x lower than Neural ODE. The Hybrid QC-HEA also exhibits the tightest cost distribution across 50 runs on L96, demonstrating superior operational reliability compared to all competing methods. Conversely, all-quantum VQE-based methods with no refinement by classical methods scale to cost 32 and 75x more than classical on L96, and thus gradient-free quantum optimisation without the classical BFGS refinement step is ultimately impractical to high-precision data assimilation and the classical BFGS refinement step is in any case a fundamental element of the architecture. Computational scaling analysis reveals that Classical 4DVAR wall-clock time grows 126-fold from L63 to L96, consistent with theoretical predictions of exponentially increasing complexity in chaotic optimisation landscapes, while the hybrid framework maintains near-classical accuracy at both scales. These results constitute an empirical proof-of-concept for hybrid quantum-classical data assimilation on realistic atmospheric models, establishing a reproducible benchmarking framework for future investigation on near-term quantum processors based NISQ devices.
We propose a novel hybrid quantum-classical framework that integrates the Quantum Approximate Optimization Algorithm (QAOA) and Quantum-enhanced Markov Chain Monte Carlo (QMCMC) with variational particle filters to tackle the computational challenges in Four-Dimensional Variational Data Assimilation (4DVAR). 4DVAR, widely used in numerical weather prediction, suffers from inefficiencies in high-dimensional, non-linear systems. Our approach, the Quantum Variational Particle Filter (QVPF), uses QAOA to optimize particle proposals and QMCMC to efficiently compute particle weights and resample, accelerating convergence while reducing the computational load. The QVPF framework addresses the curse of dimensionality by minimizing the number of particles required for accurate state estimation, thus improving efficiency in systems with complex dynamics. The hybrid model offers enhanced accuracy by integrating quantum algorithms into the variational particle filter, making it particularly suited for applications in climate modeling, space weather prediction, and defense. The potential for achieving unprecedented resolution in predictive models could transform sectors that rely on high-resolution forecasting. We present the mathematical foundations of the approach, along with discussions on algorithmic implementation and hardware requirements. Early results suggest that this hybrid framework could significantly improve data assimilation, with future implementations on near-term quantum devices offering a practical pathway for scaling up. This work demonstrates how quantum computing can address the growing need for more accurate and computationally feasible methods in large-scale data assimilation.
Time-series forecasting is vital across sectors such as finance, energy, and environmental science, where accurate future predictions drive informed decision-making. Traditional statistical methods and deep learning models like LSTM and Transformers, while effective, often struggle with high-dimensional data and long-term dependencies. In this paper, we propose a hybrid quantum-classical model that utilizes Parameterized Quantum Circuits (PQCs) to capture complex temporal patterns in multivariate time-series data. Our architecture integrates a classical encoder, a quantum variational processor, and a classical decoder, trained end-to-end using gradient-based optimization. Experiments conducted on benchmark datasets—electricity load, stock prices, and weather forecasting—demonstrate that the hybrid model consistently outperforms classical baselines in terms of Mean Squared Error (MSE), Mean Absolute Error (MAE), and R² score. Robustness analysis confirms the model’s resilience to moderate quantum noise, while an ablation study highlights the performance gain from quantum components. This work showcases the potential of hybrid quantum-classical approaches on Noisy Intermediate-Scale Quantum (NISQ) devices and lays a foundation for scalable, real-world quantum machine learning applications.
Parameter estimation is a fundamental challenge in the calibration of ordinary differential equation (ODE) models, where repeated numerical integration can lead to high computational cost. In this work, we investigate whether quantum algorithms can be leveraged to assist parameter estimation in nonlinear dynamical systems. We develop a hybrid classical-quantum framework that reformulates a data-assimilation-augmented parameter estimation problem as a combinatorial optimization task. Model dynamics and data assimilation are enforced entirely on the classical side, while the resulting parameter estimation cost functional is discretized and approximated by a quadratic unconstrained binary optimization (QUBO) surrogate. This surrogate is mapped to an Ising Hamiltonian, and quantum optimizers are used to search for low-energy configurations corresponding to candidate parameter estimates. We apply the framework to SIS and SIR epidemic models, the chaotic Lorenz-63 system, and a high-dimensional two-layer Lorenz-96 system. In this setting, the method is used to recover classical system parameters from partial state observations across steady-state, chaotic, and high-dimensional multiscale dynamical systems. Numerical experiments with synthetic data show that the proposed approach accurately recovers parameters while requiring data-assimilation solves only on a prescribed coarse grid. The framework avoids quantum state tomography, illustrating a viable pathway for integrating quantum optimization into data-driven parameter estimation for nonlinear dynamical systems.
Forecasting weather is critical in different application sectors and affects decision-making and resource distribution. Long Short-Term Memory (LSTM) models are popular, but they can be improved even further with the use of quantum computing techniques. This paper discusses a Quantum Long Short-Term Memory (QLSTM) simulated in PennyLane-based simulators. According to the experimental results, the suggested QLSTM model produced a mean absolute error (MAE) of 0.009066, a test mean square error (MSE) of 0.000162, and a coefficient of determination (R2) of 0.999846, surpassing both quantum models and classical baselines. These results highlight the potential of quantum-assisted architectures to improve accuracy in weather prediction. The research advances weather forecasting and contributes to quantum computing applications, guiding researchers in developing precise weather prediction models and enhancing decision-making in weather-sensitive domains. The proposed 4-qubit quantum model was tested with noise models, and it demonstrated high learning efficiency and strong robustness against realistic NISQ-level noise, maintaining stable optimization and low error even under moderate perturbations. • Quantum LSTM Development: The classical LSTM was extended into the quantum domain using Variational Quantum Circuits (VQCs) for feature extraction and data compression, applied to weather prediction tasks. • Experimental Evaluation: Three QLSTM variants (4, 6, and 8 qubit) were tested on two weather datasets and compared with classical LSTM and state-of-the-art QLSTM models. • Performance and Robustness: The QLSTM models outperformed baseline models, with the 4-qubit model showing strong learning efficiency and robustness under realistic NISQ-level noise.
We present a quantum-enhanced deep learning framework for short-term forecasting of extreme convective weather systems, specifically targeting the formation of bow echo structures through prediction clouds. Our approach integrates a quantum convolutional neural network (QCNN) into a classical convolutional neural network-long short-term memory (CNN-LSTM) pipeline, incorporating a 10-qubit variational quantum circuit executed on the lightning.qubit simulator. The model is trained using heterogeneous meteorological data (satellite images, convective available potential energy (CAPE) fields, lightning activity) from the extreme storm that hit the Corsican coast on August 18, 2022, preceding the convective event and evaluated during the critical intensification window (0700–0800 h). We compare this hybrid quantum model with classical CNN-LSTM and CNN-LSTM-Transformer architectures using three complementary metrics: Root mean squared error (RMSE), structural similarity index (SSIM), and Wasserstein distance. The quantum model demonstrates superior robustness to input noise and adversarial perturbations fast gradient sign method (FGSM), maintaining spatial coherence and stable prediction under degradation. These findings highlight the capacity of quantum circuits to encode more resilient representations for meteorological inference. This study provides a concrete application of hybrid QCNN architectures in the domain of extreme weather forecasting and lays the groundwork for future integration of topological data analysis to assess the preservation of topological features in quantum predictions.
Introduction Accurate prediction of hurricane tracks, intensity, and rapid intensification remains a major challenge in meteorological forecasting. This study investigates whether a hybrid quantum-classical approach, called the Quantum-Enhanced Neural Network (QENN), can improve tropical cyclone prediction. Methods QENN combines atmospheric features from multiple sources with a four-layer, 50-qubit variational circuit, grouped Pauli measurements, and a classical temporal prediction model. The evaluation included 847 Atlantic tropical cyclones recorded between 1980 and 2024. Separate hurricane-disjoint partitions were used for model development, validation, testing, and the 2024 holdout evaluation. Model reliability was further examined through ten random-seed runs, storm-level bootstrap confidence intervals, calibration analysis, comparisons with recent forecasting models, and a width-matched classical ablation study. Results On the locked 2016–2023 test set, QENN achieved a 120-h track mean absolute error of 83.7 km (95% confidence interval [CI]: 78.9–88.6 km), compared with 312.0 km (95% CI: 299.6–325.1 km) for the operational classical ensemble, representing a 73.2% reduction in relative error. For rapid-intensification prediction, QENN achieved a balanced accuracy of 94.7% (95% CI: 91.2%–97.1%), while the classical baseline achieved 67.3%. The median wall-clock time was 50.0 min for QENN and 210.0 min for the classical ensemble, equivalent to a 4.20-fold speed-up and a 76.2% reduction in runtime. In the 2024 holdout evaluation, which included six storms, the mean landfall-position error was 45 km (95% CI: 39–51 km). Discussion The results indicate that quantum-enhanced correlation features may improve forecasting accuracy and computational efficiency within the proposed experimental framework. However, the runtime comparison does not establish a formal quantum computational advantage. Further testing under operational forecasting conditions and validation on quantum hardware are needed to assess the reliability, generalizability, and practical value of the approach.