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International Joint Conference on Neural Networks (IJCNN)

A Study on Quantum Reservoir Recurrent Models for Time-Constrained Volatile Sequence Forecasting

Antonello Rosato, Andrea Ceschini, Federico Succetti, Samuel Yen-Chi Chen, Massimo Panella

Published Jun 30, 2025• 1 citation
Publisher

Abstract

This paper investigates the potential of quantum-enhanced models for time series forecasting in environments where time is a fundamental constraint. The focus is on on the quantum long short term memory networks with reservoir (QR-LSTM), and our proposed novel extension, the Autoencoded Quantum Reservoir LSTM Model (QR-LSTM-AE). The QR-LSTM, while offering substantial computational benefits in terms of time and resource efficiency, incurs a slight decrease in performance relative to the fully trainable quantum LSTM model. To address this trade-off, we introduce the QR-LSTM-AE, which utilizes an autoencoder-based strategy to recover performance lost in the reservoir alone, achieving superior accuracy without the need for full retraining. This approach not only maintains the efficiency of the QR-LSTM but also significantly reduces the computational cost associated with adapting to new data or time series, making it ideal for real-time forecasting applications. The experiments are carried out on a energy-related, highly volatile dataset, and results underscore the importance of balancing predictive accuracy with computational efficiency, highlighting the potential of quantum models to offer practical solutions in time-constrained environments. Our findings demonstrate that the QR-LSTM-AE effectively balances predictive accuracy and computational efficiency, paving the way for future advancements in quantum-enhanced forecasting through self-adaptive models, quantum autoencoders, and attention-based reservoir computing.

DOI
10.1109/ijcnn64981.2025.11228258

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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.
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The integration of quantum computing into classical machine learning architectures has emerged as a promising approach to enhance model efficiency and computational capacity. In this work, we introduce the Quantum Kernel-Based Long Short-Term Memory (QK-LSTM) network, which utilizes quantum kernel functions within the classical LSTM framework to capture complex, non-linear patterns in sequential data. By embedding input data into a high-dimensional quantum feature space, the QK-LSTM model reduces the reliance on large parameter sets, achieving effective compression while maintaining accuracy in sequence modeling tasks. This quantum-enhanced architecture demonstrates efficient convergence, robust loss minimization, and model compactness, making it suitable for deployment in edge computing environments and resource-limited quantum devices (especially in the NISQ era). Benchmark comparisons reveal that QK-LSTM achieves performance on par with classical LSTM models, yet with fewer parameters, underscoring its potential to advance quantum machine learning applications in natural language processing and other domains requiring efficient temporal data processing.
This study explores quantum and classical hybrid architectures for financial time-series fore casting, focusing on Quantum Long Short-Term Memory (QLSTM) networks and Quantum Reservoir Computing (QRC), using univariate and multivariate lag structures on real financial data. We assess how lag embeddings affect predictive accuracy and robustness. Data are en coded into quantum states via amplitude encoding, enabling efficient representation of normalized lagged observations under realistic qubit constraints. The recurrent dynamics of QLSTM and the reservoir of QRC are implemented as parameterized quantum circuits, while classical optimizers train the readout and, where applicable, variational circuit parameters. We benchmark quantum models against classical LSTM and reservoir computing using common error like metrics. Our results show that, with suitable lag selection and amplitude encoding, quantum-enhanced archi tectures match classical baselines in univariate settings and can modestly outperform them in multivariate regimes with correlated inputs, where expressive encodings are most beneficial.
Self-attention mechanisms, central to Transformer architectures, have become foundational in the development of large language models (LLMs) and various advanced machine learning systems. These mechanisms are pivotal for effectively capturing complex data dependencies and relationships, which is crucial for tasks such as natural language understanding and generation. However, as dimensionality increases, self-attention mechanisms face significant challenges related to computational efficiency and scalability. This paper introduces an encoding-based quantum self-attention mechanism designed to address these issues by embedding classical data into quantum states. This approach facilitates more efficient computation and reduces model complexity. To further enhance performance for real-world applications, particularly in financial time series forecasting, we propose a hybrid model that integrates Long Short-Term Memory (LSTM) networks with quantum self-attention mechanism. Given the constraints of the Noisy Intermediate-Scale Quantum (NISQ) era, this hybrid approach represents a plausible solution, leveraging the strengths of both classical and quantum methods and focusing on achieving faster convergence. Experimental results demonstrate that our approach converges significantly quicker than traditional models, showcasing the advantages of integrating quantum techniques with classical machine learning for practical applications.
Short-term load forecasting is essential for reliable energy management, but practical deployment on edge devices requires models that remain accurate under limited memory, finite measurement budgets, and hardware noise. This work proposes a hardware-efficient Quantum Reservoir Computing (QRC) framework for energy load forecasting, where a fixed quantum reservoir transforms temporal input windows into high-dimensional features and only a classical Elastic Net readout is trained. To reduce deployment cost, the trained readout is compressed using post-training fixed-point quantization at bit widths from 8 to 2 bits. The framework is evaluated on the Tetouan and Spain energy load datasets under exact statevector simulation, 512-shot finite sampling, and realistic hardware-noise models from IBM FakeTorino and IBM FakeMarrakesh. Results show that 6-bit readout precision preserves full-precision forecasting performance while reducing readout memory by 81.2%. Below this point, degradation becomes dataset dependent, with Tetouan showing stronger sensitivity and Spain degrading more gradually. Hardware-noise validation further shows that the trained readout transfers to noisy reservoir states without retraining. These findings support quantized QRC as a resource-aware forecasting approach for near-term quantum time-series applications.