Time-series forecasting plays a pivotal role in domains such as traffic prediction, financial analysis, and energy consumption monitoring. However, real-world time series often exhibit intertwined patterns-trends, seasonality, and latent structures-that pose significant challenges to forecasting accuracy. This paper proposes a novel forecasting model named QFreqFormer, which stands for Quantum Frequency Transformer. It combines the Quantum Fourier Transform (QFT) with a Dual-Layer Graph Attention Network (D-PAD) to effectively tackle the complexities of time-series forecasting. The QFT module exploits quantum parallelism and superposition to decompose time-series data into frequency components, offering a compact spectral representation. To further enhance the model's ability to capture intricate multi-frequency patterns, we propose the Quantum Frequency Decomposition-Reconstruction (Q-FR-Q) module, which progressively separates high- and low-frequency components using quantum parallel processing. The D-PAD framework integrates Graph Convolutional Networks (GCNs) with attention mechanisms to dynamically model temporal dependencies across frequency layers. Experimental results on benchmark datasets demonstrate that the proposed model consistently outperforms state-of-the-art methods in terms of Mean Squared Error (MSE) and Mean Absolute Error (MAE) across various horizons. In addition, the model demonstrates strong transfer learning capability, underscoring its robustness and generalizability across heterogeneous forecasting scenarios. This study introduces a quantum-enhanced deep learning framework that improves both forecasting accuracy and computational efficiency, offering practical advantages in real-world applications.
Time-series forecasting plays a pivotal role in domains such as traffic prediction, financial analysis, and energy consumption monitoring. However, real-world time series often exhibit intertwined patterns-trends, seasonality, and latent structures-that pose significant challenges to forecasting accuracy. This paper proposes a novel forecasting model named QFreqFormer, which stands for Quantum Frequency Transformer. It combines the Quantum Fourier Transform (QFT) with a Dual-Layer Graph Attention Network (D-PAD) to effectively tackle the complexities of time-series forecasting. The QFT module exploits quantum parallelism and superposition to decompose time-series data into frequency components, offering a compact spectral representation. To further enhance the model's ability to capture intricate multi-frequency patterns, we propose the Quantum Frequency Decomposition-Reconstruction (Q-FR-Q) module, which progressively separates high- and low-frequency components using quantum parallel processing. The D-PAD framework integrates Graph Convolutional Networks (GCNs) with attention mechanisms to dynamically model temporal dependencies across frequency layers. Experimental results on benchmark datasets demonstrate that the proposed model consistently outperforms state-of-the-art methods in terms of Mean Squared Error (MSE) and Mean Absolute Error (MAE) across various horizons. In addition, the model demonstrates strong transfer learning capability, underscoring its robustness and generalizability across heterogeneous forecasting scenarios. This study introduces a quantum-enhanced deep learning framework that improves both forecasting accuracy and computational efficiency, offering practical advantages in real-world applications.
Time series forecasting is a critical problem with applications in various fields, such as finance, energy, and environmental science. While classical machine learning methods have shown significant progress in this domain, the advent of quantum machine learning introduces a new perspective to address the complexities of time series prediction. In this research, we propose a novel Quantum Neural Network (QNN) approach for time series forecasting, leveraging the unique capabilities of quantum computing to capture intricate temporal dependencies and exploit quantum parallelism. By encoding time series data into quantum states and designing quantum circuits for processing, the QNN aims to achieve improved predictive accuracy compared to classical neural networks. Through extensive experiments on diverse time series datasets, we demonstrate the potential of our QNN framework and discuss the future prospects of quantum-powered time series prediction in real-world applications.
QCAAPatchTF is a quantum attention network integrated with an advanced patch-based transformer, designed for multivariate time series forecasting, classification, and anomaly detection. Leveraging quantum superpositions, entanglement, and variational quantum eigensolver principles, the model introduces a quantum-classical hybrid self-attention mechanism to capture multivariate correlations across time points. For multivariate long-term time series, the quantum self-attention mechanism can reduce computational complexity while maintaining temporal relationships. It then applies the quantum-classical hybrid self-attention mechanism alongside a feed-forward network in the encoder stage of the advanced patch-based transformer. While the feed-forward network learns nonlinear representations for each variable frame, the quantum self-attention mechanism processes individual series to enhance multivariate relationships. The advanced patch-based transformer computes the optimized patch length by dividing the sequence length into a fixed number of patches instead of using an arbitrary set of values. The stride is then set to half of the patch length to ensure efficient overlapping representations while maintaining temporal continuity. QCAAPatchTF achieves state-of-the-art performance in both long-term and short-term forecasting, classification, and anomaly detection tasks, demonstrating state-of-the-art accuracy and efficiency on complex real-world datasets.
Traditional deep learning approaches that rely on analyzing single-dimensional time sequences face extraordinary challenges in predicting chaotic time sequences due to their primary properties, which include considerable nonlinearity, high sensitivity to initial conditions, and dynamic variability. This paper presents a novel prediction model for Quantum Multi-head attention (QMulti-Attn) for chaotic time sequences. The model combines a variational quantum circuit (VQC) with multi-headed self-attention mechanisms. The model is specifically designed to integrate the diversity and complexity of VQC quantum state space with multi-headed self-attention mechanisms. This enables the model to identify and handle critical dynamic features in chaotic time sequences while improving its predictive accuracy and generalization capabilities. Initially, the data that has been received is transformed into a meta group of a predetermined size. The input for QMulti-Attn consists of a multidimensional array with embedded dimensions and a time delay. The model’s capacity for chaotic time series prediction is augmented by the incorporation of the VQC. As a result, the introduction of VQC improved the model’s capacity to identify and solve intricate patterns in chaotic time sequence prediction tasks. This enhancement was achieved by maintaining the integrity of the original features and simplifying the deep network’s training process through residual connections. The long-term dependency mechanism is employed to replicate the dynamic behavior of the chaotic system. The QMulti-Attn model outperforms the Recurrent Neural Network (RNN), Time-Series Mixer (TSMixer), and Long Short-Term Memory (LSTM) models in two simulated chaotic time sequence datasets (Lorenz and Rossler) and a real chaos time sequencing dataset, Sea Clutter. The model’s standardized mean square error on the Sea Clutter test set exhibits a 7.46% relative improvement compared to TSMixer. The QMulti-Attn model synergistically integrates quantum learning with deep learning to achieve remarkable performance in predicting chaotic temporal sequences. The model is anticipated to significantly enhance our comprehension and forecasting of intricate nonlinear dynamic systems in the actual world.
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.
Atom interferometry generates heterogeneous multivariate temporal streams governed by phase evolution, fringe dynamics, control variables, and auxiliary sensing measurements. Accurate forecasting of these signals is important for predictive monitoring, phase correction, and intelligent quantum sensing, but it requires effective modeling of long-range temporal dependencies and interactions among multiple sensing sources. This paper proposes BARFI-Q, a Quantum-Enhanced Block Attention Residual Fusion framework for multivariate time-series forecasting in atom interferometry. BARFI-Q integrates patch-based embedding, dual-branch temporal modeling, hierarchical fusion, adaptive block-attention residual aggregation, and a quantum feature-mapping module. Unlike conventional Transformer-based forecasting models with fixed additive residual paths, BARFI-Q adaptively reuses cross-depth information and enhances the fused latent representation through quantum feature mapping. To respect phase periodicity, the forecasting target is represented in circular space using sine and cosine components. Experiments show that BARFI-Q consistently outperforms strong baseline models across repeated runs and different historical window sizes. Fusion ablation results further confirm the benefit of jointly modeling channel-wise and spatial feature interactions. These results indicate that multiscale temporal learning, hierarchical fusion, adaptive residual routing, and quantum-enhanced latent transformation provide an effective framework for atom-interferometric time-series forecasting.
Self-attention mechanisms, central to Transformer architectures, have become foundational in the development of large language models (LLMs) and various advanced machine learning systems. These mechanisms are pivotal for effectively capturing complex data dependencies and relationships, which is crucial for tasks such as natural language understanding and generation. However, as dimensionality increases, self-attention mechanisms face significant challenges related to computational efficiency and scalability. This paper introduces an encoding-based quantum self-attention mechanism designed to address these issues by embedding classical data into quantum states. This approach facilitates more efficient computation and reduces model complexity. To further enhance performance for real-world applications, particularly in financial time series forecasting, we propose a hybrid model that integrates Long Short-Term Memory (LSTM) networks with quantum self-attention mechanism. Given the constraints of the Noisy Intermediate-Scale Quantum (NISQ) era, this hybrid approach represents a plausible solution, leveraging the strengths of both classical and quantum methods and focusing on achieving faster convergence. Experimental results demonstrate that our approach converges significantly quicker than traditional models, showcasing the advantages of integrating quantum techniques with classical machine learning for practical applications.