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Optimizing Hybrid Quantum-Classical Models Using Parameterized Quantum Circuits for Time-Series Forecasting

Harshraj Bhoite

Published Jul 19, 2025• 0 citations
Publisher

Abstract

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.

DOI
10.36227/techrxiv.175295886.67877890/v1

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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.
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.
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<!--HTML-->Machine learning has enabled computers to learn from data and improve their performance on tasks, revolutionizing various industries by automating processes, uncovering insights, and enhancing decision-making. NISQ (Noisy Intermediate-Scale Quantum) refers to the current stage of quantum computing, characterized by quantum devices with a moderate number of qubits and significant noise. In the NISQ era, parametrized quantum circuits (PQC) are employed in machine learning as flexible quantum algorithms that can be executed on current noisy quantum devices. By introducing tunable parameters, these circuits can adapt to the limitations of NISQ devices, enabling quantum-enhanced solutions to classification and generative tasks while paving the way for practical applications of quantum machine learning. Time series arise from the abundance of sequential data in various fields, and time series analysis uncovers patterns, trends, and dependencies within the temporal data, enabling informed decision-making and predictions for a wide range of applications. In this project, we aim to replicate the findings of a paper that utilized parametrized quantum circuits (PQCs) to forecast time series data in the context of finance. By faithfully reproducing the original experiments, we seek to establish the reliability and applicability of PQCs for financial time series predictions. Building upon these results, we further investigate the impact of hyperparameters and explore novel circuit architectures to optimize the performance of quantum machine learning in 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.
Weather forecasting plays a critical role across various sectors, supporting strategic planning and reducing the impact of hazardous climatic conditions. However, the inherently chaotic and nonlinear nature of atmospheric systems limits the performance of conventional forecasting approaches, often resulting in prediction inaccuracies and heightened risk. This study proposes a quantum-driven predictive framework that exploits the computational strengths of Quantum Machine Learning (QML) and hybrid quantum–classical optimization to enhance the accuracy and efficiency of modern forecasting models. The framework employs Quantum Neural Networks (QNNs) combined with Variational Quantum Circuits (VQCs) to learn complex spatial–temporal dynamics embedded within large meteorological datasets. Through quantum feature encoding, key atmospheric indicators—including temperature, humidity, wind velocity, and barometric pressure—are projected into high-dimensional Hilbert spaces, enabling more expressive pattern extraction and robust predictive behavior. Simulation results reveal that the quantum-augmented approach surpasses traditional deep learning architectures in both training convergence and forecast precision when applied to extensive weather records. The hybrid design further supports scalability by intelligently distributing computational workloads between classical processors and quantum hardware. Overall, this research demonstrates the transformative potential of quantum computing in atmospheric modeling, offering a foundation for future real-time forecasting systems capable of managing the increasing complexity of global climate patterns.
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.