The integration of quantum computing and machine learning has led to innovative algorithms in quantum machine learning that outperform traditional methods in time series forecasting. This paper introduces the Quantum Amplitude-Phase Dropout Attention Model (QAPDAM), which combines Amplitude-Phase Decomposition (APDM) measurement and quantum dropout attention to improve prediction accuracy and robustness while minimizing circuit parameters. The QAPDAM model consists of a Variational Quantum Circuit (VQC) for predictions and an APDM-based dropout self-attention module for feature extraction. Data is encoded into quantum states and processed with a parameter-efficient APDM self-attention mechanism to calculate query, key, and value. Quantum dropout is applied to adjust attention weights dynamically, reducing overfitting and adapting to data variability. Forecasts are obtained through circuit evolution and measurement. We tested QAPDAM's performance in Electric Transformer Temperature dataset, finding it surpasses other models in terms of predictive accuracy with a 25% reduction in circuit parameters.
The integration of quantum computing and machine learning has led to innovative algorithms in quantum machine learning that outperform traditional methods in time series forecasting. This paper introduces the Quantum Amplitude-Phase Dropout Attention Model (QAPDAM), which combines Amplitude-Phase Decomposition (APDM) measurement and quantum dropout attention to improve prediction accuracy and robustness while minimizing circuit parameters. The QAPDAM model consists of a Variational Quantum Circuit (VQC) for predictions and an APDM-based dropout self-attention module for feature extraction. Data is encoded into quantum states and processed with a parameter-efficient APDM self-attention mechanism to calculate query, key, and value. Quantum dropout is applied to adjust attention weights dynamically, reducing overfitting and adapting to data variability. Forecasts are obtained through circuit evolution and measurement. We tested QAPDAM's performance in Electric Transformer Temperature dataset, finding it surpasses other models in terms of predictive accuracy with a 25% reduction in circuit parameters.
Abstract In this paper, we address the challenge of multivariate time-series forecasting through quantum-enhanced machine learning architectures. We propose adaptation strategies that extend variational quantum circuit models (VQC), traditionally constrained to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid models to systematically evaluate their ability to capture cross-variable dependencies. Building on these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Finally, we present a comprehensive empirical evaluation on both synthetic and real-world datasets, demonstrating that quantum-enhanced models can achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines. These findings highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.
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.
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.
This paper explores the application of quantum self-adaptive learning to high-dimensional time series forecasting models, leveraging the unique properties of quantum computing to enhance prediction accuracy and efficiency, particularly in scenarios involving large datasets and complex feature representations. We propose a novel "Quantum Adaptive Adjustment" mechanism that dynamically adjusts the learning process based on the characteristics of the time series data, leading to improved model performance. The research focuses on mitigating the limitations of traditional machine learning algorithms in handling high dimensionality and complex patterns, presenting a promising approach for improved forecasting capabilities. The paper details the implementation of the quantum self-adaptive learning process, including the introduction of the adaptive adjustment mechanism and a comprehensive evaluation of its effectiveness through simulations and a benchmark dataset. We conclude with a discussion of the potential impact of this approach on various real-world time series forecasting tasks.
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.
In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid architectures to systematically evaluate their capacity to model cross-variable dependencies. Second, building upon these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Third, we provide a comprehensive empirical evaluation on both synthetic and real-world datasets, showing that quantum-based models may achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines in some cases. These contributions highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.