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.
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.
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.
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.
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.
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 presents a unified quantum-classical hybrid framework for multi-horizon time-series forecasting, introducing two model variants Quantum Reservoir Forecaster (QRC-F) and Variational Quantum Forecaster (VQF-F). The proposed framework investigates the complexity-fidelity trade-off of quantum forecasting under near-term NISQ hardware constraints. Continuous time-series signals are transformed into binary representations through uniform quantization and encoded into quantum states using angle encoding with parameterized RY rotation gates. Cross-channel entanglement layers capture dependencies among multiple variables. QRC-F utilizes a fixed random unitary quantum reservoir for stable, gradient-free temporal feature extraction, whereas VQF-F employs a trainable variational quantum circuit optimized through the parameter-shift rule to learn temporal and inter-variable patterns from Pauli expectation values. Both models replace computationally expensive quadratic self-attention with efficient linear transformations, reducing parameter complexity. A shared MIMO-based multi-horizon prediction head simultaneously generates forecasts across multiple horizons, avoiding error accumulation in recursive forecasting. Experimental evaluations on benchmark datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Weather, electricity, and exchange-rate, demonstrate that VQF-F achieves superior training stability and parameter efficiency, while QRC-F provides enhanced robustness and circuit fidelity under quantum noise. The results establish a practical quantum-native forecasting framework with strong potential for deployment on near-term NISQ devices.
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.