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International Forum on Electrical Engineering and Automation (IFEEA)

Quantum neural network based on self-attention mechanism optimized by quantum annealing Time series forecasting of power load

Baonan Wang, Youdian Fan

Published Nov 7, 2025• 0 citations
Publisher

Abstract

Accurate power load forecasting is vital for reliable grid operation and energy management. We propose QRNN-QA-MSSA, which builds a Quantum Recurrent Neural Network (QRNN) via Automatic Differentiation Quantum Circuits (ADQC), applies quantum annealing (QA) for global optimization, and integrates multi-scale self-attention (MSSA) to capture short-and long-term dependencies. Evaluated on four seasonal datasets against RNN, LSTM, QRNN, QRNN-QA, and QRNN-QA-SA, the proposed model achieves average RMSE = 0.017 and MAPE = 3.28%, improving over QRNN-QA by about 20.8% and 18.0%, and reducing errors by >40% compared with classical RNN and LSTM. It also converges faster with smoother error curves. The average R2reaches 99.49%, and the model maintains high accuracy under pronounced peak–valley load intervals. These results indicate that coupling quantum annealing with multi-scale attention is an effective route to optimizing quantum neural networks for complex seasonal time-series forecasting.

DOI
10.1109/ifeea66847.2025.11388395

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Accurate power load forecasting is vital for reliable grid operation and energy management. We propose QRNN-QA-MSSA, which builds a Quantum Recurrent Neural Network (QRNN) via Automatic Differentiation Quantum Circuits (ADQC), applies quantum annealing (QA) for global optimization, and integrates multi-scale self-attention (MSSA) to capture short-and long-term dependencies. Evaluated on four seasonal datasets against RNN, LSTM, QRNN, QRNN-QA, and QRNN-QA-SA, the proposed model achieves average RMSE = 0.017 and MAPE = 3.28%, improving over QRNN-QA by about 20.8% and 18.0%, and reducing errors by >40% compared with classical RNN and LSTM. It also converges faster with smoother error curves. The average R2reaches 99.49%, and the model maintains high accuracy under pronounced peak–valley load intervals. These results indicate that coupling quantum annealing with multi-scale attention is an effective route to optimizing quantum neural networks for complex seasonal time-series forecasting.
Time series forecasting remains a significant challenge in various domains, including finance, weather prediction, and industrial process control. Traditional neural networks, particularly recurrent neural networks (RNNs), often struggle to effectively capture the intricate temporal dependencies inherent in time series data. This paper proposes a novel approach leveraging quantum-inspired algorithms to optimize RNNs for improved time series forecasting performance. Specifically, we explore the utilization of quantum annealing techniques to adjust the weights within an RNN architecture. This approach mimics key quantum principles, such as superposition and interference, to potentially enhance the network's ability to represent and predict complex temporal patterns. The core claim of this work is that classical neural networks, particularly RNNs, are limited in their ability to model temporal dependencies. We introduce a mechanism where quantum-inspired algorithms, particularly quantum annealing, are employed to optimize the weights of RNNs. The underlying principles of superposition and interference are leveraged to capture more complex temporal patterns. The results demonstrate the potential of this quantum-inspired approach to achieving superior forecasting accuracy compared to conventional RNNs.
Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.
Traditional deep learning approaches that rely on analyzing single-dimensional time sequences face extraordinary challenges in predicting chaotic time sequences due to their primary properties, which include considerable nonlinearity, high sensitivity to initial conditions, and dynamic variability. This paper presents a novel prediction model for Quantum Multi-head attention (QMulti-Attn) for chaotic time sequences. The model combines a variational quantum circuit (VQC) with multi-headed self-attention mechanisms. The model is specifically designed to integrate the diversity and complexity of VQC quantum state space with multi-headed self-attention mechanisms. This enables the model to identify and handle critical dynamic features in chaotic time sequences while improving its predictive accuracy and generalization capabilities. Initially, the data that has been received is transformed into a meta group of a predetermined size. The input for QMulti-Attn consists of a multidimensional array with embedded dimensions and a time delay. The model’s capacity for chaotic time series prediction is augmented by the incorporation of the VQC. As a result, the introduction of VQC improved the model’s capacity to identify and solve intricate patterns in chaotic time sequence prediction tasks. This enhancement was achieved by maintaining the integrity of the original features and simplifying the deep network’s training process through residual connections. The long-term dependency mechanism is employed to replicate the dynamic behavior of the chaotic system. The QMulti-Attn model outperforms the Recurrent Neural Network (RNN), Time-Series Mixer (TSMixer), and Long Short-Term Memory (LSTM) models in two simulated chaotic time sequence datasets (Lorenz and Rossler) and a real chaos time sequencing dataset, Sea Clutter. The model’s standardized mean square error on the Sea Clutter test set exhibits a 7.46% relative improvement compared to TSMixer. The QMulti-Attn model synergistically integrates quantum learning with deep learning to achieve remarkable performance in predicting chaotic temporal sequences. The model is anticipated to significantly enhance our comprehension and forecasting of intricate nonlinear dynamic systems in the actual world.
Time series forecasting is vital in many fields, including energy demand prediction and financial markets. Long Short-Term Memory (LSTM) networks have demonstrated strong performance in capturing temporal dependencies in sequential data. However, traditional LSTM face challenges such as vanishing gradients and limited capabilities in modeling long-term dependencies, especially with complex, high-dimensional data. The model integrates Variable Quantum Circuit (VQC) into a modified LSTM (mLSTM) structure, taking advantage of quantum properties such as superposition and entanglement to improve memory retention and computational efficiency. We would like to introduce modified Quantum Long Short-Term Memory (mQLSTM), which is specifically designed for photovoltaic (PV) energy forecasting. Key improvements include a quantum memory mechanism that mitigates loss of information over extended sequences, a redesigned forget gate to enhance long-term learning and an Exponentially Weighted Feature (EWF) layer to accelerate convergence and enhance generalization. This paper highlights the potential of quantum-enhanced deep learning architectures to advance time series forecasting and opens new directions for practical applications in renewable energy and beyond.
Abstract Modeling temporal dependencies within quantum systems remains a key challenge for quantum machine learning. Current quantum neural networks largely depend on classical recurrent modules, which introduce optimization bottlenecks and coherence loss during sequence processing. To address this, we propose a fully quantum-native recurrent neural network (QRNN) for end-to-end sequential learning. Our architecture captures temporal dynamics through coherent unitary operations, avoiding external classical recurrence and mid-circuit state collapse. The proposed model was benchmarked against a classical recurrent neural network (RNN), quantum tensor networks, and state-of-the-art hybrid QRNN using the Origin Quantum superconducting platform. Experimental evaluations on nonlinear functions, complex dynamical systems, and meteorological datasets demonstrate that our quantum-native QRNN achieves improved prediction accuracy and exhibits enhanced capability in forecasting complex temporal features. For instance, on the relative humidity forecasting task, the proposed QRNN achieves a 73.5% reduction in Root mean square error compared to the hybrid VQRNN. This work establishes a robust framework for preserving coherence in pure quantum sequential processing, offering a scalable path for time-series forecasting on near-term quantum hardware.
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.