We propose a single-qubit Quantum Machine Learning (QML) model for time series forecasting, built around the concept of a Quantum Reupload Unit (QRU), a hardwareefficient quantum circuit architecture with shallow depth. The proposed model demonstrates enhanced predictive power compared to variational methods such as quantum circuits (VQC), parameterized quantum circuits (PQC), and quantum residual blocks (QRB). The proposed QRU outperforms classical learning models such as Recurrent Neural Networks (RNNs) and Long-Short Term Memory (LSTM) with the same number of parameters. The novelty of this approach is its ability to model temporal patterns without relying on an extensive memory state, which reduces resource demands while preserving forecast accuracy. The expressivity of the model is evaluated through Fourier spectral decomposition. We analyze the trainability of our model using the absorption witness metric. We benchmarked the proposed model on the Mackey-Glass chaotic time series and the real-world river level dataset from TAIAO. The proposed model consistently exhibits enhanced expressivity over both of the datasets. These results highlight the significance of QRUs as promising candidates for learning models that can be conveniently deployed on noisy intermediate-scale quantum (NISQ) hardware.
We propose a single-qubit Quantum Machine Learning (QML) model for time series forecasting, built around the concept of a Quantum Reupload Unit (QRU), a hardwareefficient quantum circuit architecture with shallow depth. The proposed model demonstrates enhanced predictive power compared to variational methods such as quantum circuits (VQC), parameterized quantum circuits (PQC), and quantum residual blocks (QRB). The proposed QRU outperforms classical learning models such as Recurrent Neural Networks (RNNs) and Long-Short Term Memory (LSTM) with the same number of parameters. The novelty of this approach is its ability to model temporal patterns without relying on an extensive memory state, which reduces resource demands while preserving forecast accuracy. The expressivity of the model is evaluated through Fourier spectral decomposition. We analyze the trainability of our model using the absorption witness metric. We benchmarked the proposed model on the Mackey-Glass chaotic time series and the real-world river level dataset from TAIAO. The proposed model consistently exhibits enhanced expressivity over both of the datasets. These results highlight the significance of QRUs as promising candidates for learning models that can be conveniently deployed on noisy intermediate-scale quantum (NISQ) hardware.
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.
Quantum data reuploading models can increase the expressive capacity of variational quantum models, but do not necessarily improve predictive performance. In the present work, we investigate this behavior for seasonal time series forecasting and show that data encoding determines how well temporal structures are represented as circuit depth increases. We develop a fidelity-based quantum geometric description in which repeated encodings contribute to an effective input generator, so that reuploading depth changes the quantum geometry through which approximately recurrent inputs are distinguished. We construct fixed and adaptive seasonal encodings that represent observation magnitude and seasonal phase in distinct Bloch-sphere coordinates. We evaluate these encodings for monthly precipitation derived from ERA5-Land, a global reanalysis dataset, from a representative semi-arid, drought-prone tropical region in East Africa, using a 14-month lag window and reuploading depths L= 1-6. We find that in ideal simulations, standard value-based encodings degrade markedly with depth, whereas adaptive seasonal encodings preserve temporal correlation, spectral structure, and forecasting accuracy. Noisy simulations show that this encoding hierarchy persists at shallow and intermediate depths, while larger depths are limited by circuit noise and optimization difficulty. The seasonal quantum models remain competitive with established classical forecasting methods (ARIMA, random forests, and LSTMs). These results identify structure-aware quantum data encoding as a general strategy for building deeper quantum reuploading models.
The rapid growth of modern machine learning (ML) models presents fundamental challenges in parameter efficiency and computational resource requirements. This study introduces the Quantum Recurrent Unit (QRU), a novel quantum neural network (NN) architecture specifically designed to address these challenges while remaining compatible with Noisy Intermediate-Scale Quantum (NISQ) devices. QRU leverages quantum controlled-SWAP (C-SWAP; Fredkin) gates to implement an information selection mechanism inspired by classical Gated Recurrent Units (GRUs), enabling selective processing of temporal information via quantum operations. Through its innovative recurrent architecture featuring measurement results feedforward state propagation and shared parameters across time steps, QRU achieves constant circuit depth and constant parameter count regardless of input sequence length, effectively circumventing stringent NISQ hardware constraints. We systematically validate QRU through three progressive experiments: (1) oscillatory behavior prediction, where 72-parameter QRU matches 197-parameter classical GRU performance; (2) Wisconsin Diagnostic Breast Cancer classification, where 35 parameters achieve 96.13% accuracy comparable to 167-parameter artificial NNs; and (3) MNIST handwritten digit recognition, where 132 parameters reach 98.05% accuracy, outperforming a 27,265-parameter convolutional NN. These results demonstrate that QRU consistently achieves comparable or superior performance with significantly fewer parameters than classical NNs while maintaining constant quantum circuit depth. The architecture's quantum-native design, combining C-SWAP-based information selection with novel recurrent processing, suggests QRU's potential as a fundamental building block for next-generation ML systems, offering a promising pathway toward more efficient and scalable quantum ML architectures.
Abstract In this work, we explore the application of 1D quantum convolutional layers for time series forecasting, framing the problem within the context of machine learning and quantum circuit expressivity. By encoding multiple time steps as features into a quantum circuit, the forecasting task becomes intrinsically multidimensional. We leverage the recent theoretical results that describe Variational Quantum Circuits (VQCs) as multidimensional Fourier series, to design a more expressive 1D quantum convolutional neural network in which an enhanced performance is obtained by reuploading the data. We aim to relate the number of accessible coefficients in each architecture design with the obtained metrics. Our analysis incorporates key machine learning concepts such as expressivity and the presence of barren plateaus, evaluating their impact on generalization and training efficiency. Notably, we show that even with a limited number of trainable parameters, quantum circuits can approximate high-degree Fourier functions, underscoring their expressive capacity and computational efficiency. Our results demonstrate that more expressive ansatz, characterized by richer Fourier spectra, consistently yield improved predictive performance as the number of qubits increases. This study bridges theoretical insights from quantum physics with practical advances in machine learning model design for time series forecasting.
Quantum Machine Learning (QML) presents as a revolutionary approach to weather forecasting by using quantum computing to improve predictive modeling capabilities. In this study, we apply QML models, including Quantum Gated Recurrent Units (QGRUs), Quantum Neural Networks (QNNs), Quantum Long Short-Term Memory(QLSTM), Variational Quantum Circuits(VQCs), and Quantum Support Vector Machines(QSVMs), to analyze meteorological time-series data from the ERA5 dataset. Our methodology includes preprocessing meteorological features, implementing QML architectures for both classification and regression tasks. The results demonstrate that QML models can achieve reasonable accuracy in both prediction and classification tasks, particularly in binary classification. However, challenges such as quantum hardware limitations and noise affect scalability and generalization. This research provides insights into the feasibility of QML for weather prediction, paving the way for further exploration of hybrid quantum-classical frameworks to enhance meteorological forecasting.
Accurate load forecasting is critical for effective energy management, infrastructure planning, and ensuring the stability of modern power systems. With growing interest in Quantum Computing (QC), recent efforts have demonstrated the applicability of Quantum Machine Learning (QML) across various domains, including supervised and unsupervised learning. However, the use of QML models for Time Series Forecasting (TSF) remains relatively underexplored. In this work, we present a complete framework for TSF based on Variational Quantum Algorithms (VQAs), capable of both single-step and multi-step ahead forecasting. We use tensor product encoding to encode the classical input samples into quantum states, and use the data re-uploading strategy to introduce temporal dependencies across each layer of the quantum circuit. Within this framework, we systematically evaluate multiple Variational Quantum Circuit (VQC) architectures to assess their suitability for forecasting problem. Among the tested configurations, thenLocaland its modified variantQuReUpconsistently outperformed other quantum ansatz designs. Notably, in recursive multi-step forecasting scenarios, these models not only matched but surpassed the performance of a classical Artificial Neural Network (ANN). For example, thenLocalmodel achieved a 8% reduction in mean absolute error (MAE) over ANN for a 24-hour horizon. These results underscore the potential of VQAs for efficient and accurate TSF, particularly in scenarios requiring short to medium-term predictions. The proposed framework offers a promising foundation for future research, including extensions to diverse datasets and deployment on real quantum hardware to study the impact of quantum noise and scalability.