Time series forecasting largely benefits from combining the strengths of different models, especially using a scheme where a model corrects another model by capturing supplementary patterns from forecasting errors. Concurrently, quantum models are providing a means to augment the classical capacity, including in time series forecasting, by acting alongside classical models in hybrid architectures. In this work, we propose the first forecasting system based on error correction that jointly uses quantum and classical models. Here, quantum models first extract patterns by exploring quantum phenomena, and classical models capture the remaining patterns from the quantum errors. Compared to classical single models and classical-classical hybrid models based on error correction, the complementary capacity that emerges from this quantum-classical system provided the best results in most of the addressed problems. Therefore, this work paves the way to introduce quantum models in established hybridization schemes for time series forecasting.
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Submitted to Nature Computational Science. 24 pages, 10 figures
Time series forecasting largely benefits from combining the strengths of different models, especially using a scheme where a model corrects another model by capturing supplementary patterns from forecasting errors. Concurrently, quantum models are providing a means to augment the classical capacity, including in time series forecasting, by acting alongside classical models in hybrid architectures. In this work, we propose the first forecasting system based on error correction that jointly uses quantum and classical models. Here, quantum models first extract patterns by exploring quantum phenomena, and classical models capture the remaining patterns from the quantum errors. Compared to classical single models and classical-classical hybrid models based on error correction, the complementary capacity that emerges from this quantum-classical system provided the best results in most of the addressed problems. Therefore, this work paves the way to introduce quantum models in established hybridization schemes for time series forecasting.
Time-series forecasting is essential for strategic planning and resource allocation, and is important in areas like finance, supply chain management, and energy demand prediction.In such areas, small improvements in forecast quality can lead to significant economic and strategic benefits.It is important to assess the practicality of quantum-enhanced forecasting methods because quantum approaches can complement the strengths of classical models.In this work, we explore two quantum-based approaches for time-series forecasting.The first approach utilizes a parameterized quantum circuit (PQC) model.The second approach employs variational quantum linear regression (VQLS), formulating the forecasting problem as a system of linear equations solved via quantum optimization.A comparative analysis is conducted to assess their practical applicability and performance.In our experiments, the PQC with COBYLA optimization achieved the lowest test error rates, outperforming the classical baselines under the reported settings.VQLS formulation faced stability issues on general synthetic datasets.
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.
Prediction of stock price remains a challenging task because financial markets are dynamic and often non-linear, unpredictable patterns. To deal with such unpredictable data, the architecture that’s created must identify both time based trends and hidden patterns in data. In this study, we explore a hybrid modelling approach by combining both the classical deep learning techniques with quantum computing principles. Specifically, a Long Short-Term Memory (LSTM) is combined with a Quantum Neural Network (QNN) to understand the benefits of using quantum in time series forecasting. Rather than depending on a single quantum configuration, multiple feature maps and ansatz circuit designs were evaluated to identify the most suitable arrangement for the QLSTM model. Resultant framework blends ideas from both classical computing and quantum approaches to improve how we predict patterns over time in real-life scenarios.
Hybrid quantum–classical computing has become an attractive strategy for improving learning capability and predictive capacity in complex data environments. This work presents a Python-Integrated framework for smart time-series prediction using quantum and classical computation in a single process. The method uses the Qiskit for developing unpredictable quantum systems which store sequential financial data through calculated rotation gates and entanglement layers. A classical optimizer operating in Python performs gradient-based updates on the hybrid loss function, enabling stable convergence within fewer training epochs. The comparison with conventional neural networks demonstrates a higher prediction accuracy of 93.7 percent compared to 89.3 percent for the classical model, along with a 22 percent reduction in training time and 18 percent lower execution latency. Mean-Squared error (MSE) reached 0.014 with a correlation coefficient of 0.92, indicating reliable trend capture in nonlinear financial patterns. Scalability tests using multi-qubit simulation on cloud-based quantum runtimes confirm consistent performance across varying data sizes. The proposed hybrid approach supports adaptive forecasting and efficient resource consumption, providing an easy way to implement real-time analytics in networked computing environments. This work shows Python’s capacity as a bridge between quantum programming and classical machine learning for future-generation predictive computing systems.
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 involves analyzing historical data to predict future trends and is useful for reducing uncertainty in various phenomena. Recurrent Neural Network-based Long Short-Term Memory (LSTM) has been shown to be used for time series forecasting. However, the introduction of a hybrid quantum-classical model of LSTM, i.e., Quantum LSTM (QLSTM), opens up avenues for faster and more efficient computing and, therefore, is of significant potential. These potentials underscore the necessity for a comparative analysis of both models to assess their effectiveness and efficiency. This study evaluates the performance of QLSTM and classical LSTM models in time series forecasting. Through controlled parametric numerical experiments, the study examines the performance of both models using CPUs and GPUs in cloud environments. Our findings reveal significant improvements in the QLSTM model, with enhanced training accuracy and reduced test loss compared to the classical LSTM under similar epochs and batch sizes. The results demonstrate the superior efficiency of the QLSTM model in handling large, complex data sets compared to the classical LSTM model.