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.
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.
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.
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.
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.
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.
Long-range time series forecasting remains challenging, as it requires capturing non-stationary and multi-scale temporal dependencies while maintaining noise robustness, efficiency, and stability. Transformer-based architectures such as Autoformer and Informer improve generalization but suffer from quadratic complexity and degraded performance on very long time horizons. State space models, notably S-Mamba, provide linear-time updates but often face unstable training dynamics, sensitivity to initialization, and limited robustness for multivariate forecasting. To address such challenges, we propose the Quantum-Optimized Selective State Space Model (Q-SSM), a hybrid quantum-optimized approach that integrates state space dynamics with a variational quantum gate. Instead of relying on expensive attention mechanisms, Q-SSM employs a simple parametrized quantum circuit (RY-RX ansatz) whose expectation values regulate memory updates adaptively. This quantum gating mechanism improves convergence stability, enhances the modeling of long-term dependencies, and provides a lightweight alternative to attention. We empirically validate Q-SSM on three widely used benchmarks, i.e., ETT, Traffic, and Exchange Rate. Results show that Q-SSM consistently improves over strong baselines (LSTM, TCN, Reformer), Transformer-based models, and S-Mamba. These findings demonstrate that variational quantum gating can address current limitations in long-range forecasting, leading to accurate and robust multivariate predictions.