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IEEE Transactions on Automation Science and Engineering

Temporally-Preserving Quantum LSTM With Multiscale Attention Mechanisms for Soft Sensor Applications

Xian-Bing Meng, Bi-Cheng Guo, Kangkang Xu, Hui Li, C. L. Philip Chen

Published Jan 1, 2026• 2 citations
Publisher

Abstract

Soft sensor modeling is the task of using measurable variables to predict target ones, which may involve nonlinearity and temporally dynamics. Despite significant progress, there is a relative lack of research on soft sensor-oriented Quantum Long Short-Term Memory (QLSTM) design and application. As a novel quantum soft sensor approach, a temporally-preserving QLSTM (TP-QLSTM) is proposed by integrating with multiscale attention mechanisms. Specifically, a temporally-preserving-based adaptive variational quantum circuit is designed by establishing entanglement across temporal inputs to improve the temporally learning capability of QLSTM. Moreover, multiscale attention mechanisms are designed in the input and output parts of TP-QLSTM to learn nonlinearities and temporal dynamics from different feature dimensions and temporal ones, as well as from historical hidden states and temporal outputs. In addition, a referential attention-based autoregressive forecasting strategy is proposed as output module of TP-QLSTM to predict the target results. Experiments on two soft sensor cases demonstrate the effectiveness and practicality of our method. Note to Practitioners—In industrial processes, soft sensors are critical for achieving comprehensive state awareness and predictive management. However, practical soft sensors often struggle with complex nonlinear and time-dependent relationships in dynamic processes. As an innovative attempt to enhance soft sensing from a quantum algorithm perspective, we propose a TP-QLSTM by integrating multiscale attention mechanisms. Through designing adaptive quantum circuits that preserve temporal correlations and incorporating multiscale attention mechanisms, our method effectively captures multiscale dynamics and nonlinearities from process data. This enables accurate and robust predictions of key variables in industrial settings. Experiments on real cases confirm that our method achieves high prediction accuracy while maintaining low computational latency—with an average inference time of less than 0.6 ms per sample. A current limitation is that the quantum algorithm is implemented using simulated quantum circuits, which restricts the full exploitation of quantum parallelism. Future work will focus on deploying the model to hardware platforms that support real quantum circuit computation, thus enabling efficient training and inference.

DOI
10.1109/tase.2026.3680978

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Soft sensor modeling is the task of using measurable variables to predict target ones, which may involve nonlinearity and temporally dynamics. Despite significant progress, there is a relative lack of research on soft sensor-oriented Quantum Long Short-Term Memory (QLSTM) design and application. As a novel quantum soft sensor approach, a temporally-preserving QLSTM (TP-QLSTM) is proposed by integrating with multiscale attention mechanisms. Specifically, a temporally-preserving-based adaptive variational quantum circuit is designed by establishing entanglement across temporal inputs to improve the temporally learning capability of QLSTM. Moreover, multiscale attention mechanisms are designed in the input and output parts of TP-QLSTM to learn nonlinearities and temporal dynamics from different feature dimensions and temporal ones, as well as from historical hidden states and temporal outputs. In addition, a referential attention-based autoregressive forecasting strategy is proposed as output module of TP-QLSTM to predict the target results. Experiments on two soft sensor cases demonstrate the effectiveness and practicality of our method. Note to Practitioners—In industrial processes, soft sensors are critical for achieving comprehensive state awareness and predictive management. However, practical soft sensors often struggle with complex nonlinear and time-dependent relationships in dynamic processes. As an innovative attempt to enhance soft sensing from a quantum algorithm perspective, we propose a TP-QLSTM by integrating multiscale attention mechanisms. Through designing adaptive quantum circuits that preserve temporal correlations and incorporating multiscale attention mechanisms, our method effectively captures multiscale dynamics and nonlinearities from process data. This enables accurate and robust predictions of key variables in industrial settings. Experiments on real cases confirm that our method achieves high prediction accuracy while maintaining low computational latency—with an average inference time of less than 0.6 ms per sample. A current limitation is that the quantum algorithm is implemented using simulated quantum circuits, which restricts the full exploitation of quantum parallelism. Future work will focus on deploying the model to hardware platforms that support real quantum circuit computation, thus enabling efficient training and inference.
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.
Accurate state-of-health (SOH) estimation for lithium-ion batteries remains a challenging problem due to complex electrochemical degradation mechanisms and long-range temporal dependencies. In this work, we propose a quantum-enhanced recurrent framework, termed QLSTM, in which variational quantum circuits are directly embedded into the gating mechanisms of long short-term memory networks. By replacing classical affine transformations with parameterized unitary operations, the proposed model introduces structured nonlinear transformations into the recurrent state-transition process. Extensive experiments on multiple benchmark battery datasets demonstrate that QLSTM consistently outperforms classical sequence models in both predictive accuracy and robustness, achieving significant reductions in mean absolute error (MAE), with improvements on the order of 20% compared with classical LSTM baselines. Ablation studies further confirm that these improvements arise primarily from quantum-enhanced gating rather than input-level transformations. Additional analyses on qubit scaling and noise robustness reveal that model performance is governed by a balance between expressive capacity and trainability. These results provide empirical evidence that embedding quantum computational primitives within recurrent architectures offers a structurally grounded approach to improving sequence modeling capability. The proposed framework establishes a new design paradigm for integrating quantum operators into temporal learning models, with potential applications in complex dynamical system prediction tasks.
Quantum machine learning (QML) offers new perspectives for modeling complex sequential data by leveraging the computational advantages of quantum computing. In this work, we explore the application of Quantum Long Short-Term Memory (QLSTM) networks for sequence prediction tasks. By integrating parameterized quantum circuits within the classical LSTM architecture, QLSTM models exploit quantum parallelism and entanglement to learn temporal dependencies in data more efficiently. We evaluate the performance of QLSTM on synthetic and real-world sequence prediction tasks and compare it with its classical counterpart. The results demonstrate that QLSTM models achieve competitive performance with fewer trainable parameters, indicating their potential as lightweight and efficient models for sequence learning and prediction.
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.
We present the Quantum Kernel-Based Long Short-Term Memory (QK-LSTM) network, which integrates quantum kernel methods into classical LSTM architectures to enhance predictive accuracy and computational efficiency in climate time-series forecasting tasks, such as Air Quality Index (AQI) prediction. By embedding classical inputs into high-dimensional quantum feature spaces, QK-LSTM captures intricate nonlinear dependencies and temporal dynamics with fewer trainable parameters. Leveraging quantum kernel methods allows for efficient computation of inner products in quantum spaces, addressing the computational challenges faced by classical models and variational quantum circuit-based models. Designed for the Noisy Intermediate-Scale Quantum (NISQ) era, QK-LSTM supports scalable hybrid quantum-classical implementations. Experimental results demonstrate that QK-LSTM outperforms classical LSTM networks in AQI forecasting, showcasing its potential for environmental monitoring and resource-constrained scenarios, while highlighting the broader applicability of quantum-enhanced machine learning frameworks in tackling large-scale, high-dimensional climate datasets.
Accurate financial volatility forecasting is crucial but challenged by the non-linear, highly correlated nature of market data. Recently, quantum computing has emerged as a promising paradigm for solving complex high-dimensional sampling problems. To harness this, we propose a novel hybrid framework combining the temporal representation power of classical neural networks with the distribution-learning capabilities of quantum models. Specifically, we integrate a Long Short-Term Memory (LSTM) network with a Quantum Circuit Born Machine (QCBM). The LSTM extracts dynamic features, while the QCBM acts as a learnable generative prior modeling complex market distributions to guide forecasting. Evaluated on 5-minute high-frequency data from the SSE Composite and CSI 300 indices, our model significantly outperforms a classical LSTM baseline across MSE, RMSE, and QLIKE metrics. Furthermore, by introducing a stochastic ``Drop-Prior" mechanism during training, the LSTM implicitly distills structured information from the quantum prior. This establishes a pragmatic paradigm of ``quantum-assisted training with classical-efficient inference", whereby the model retains its quantum-enhanced accuracy even when the quantum module is entirely disabled during deployment. This demonstrates a practical pathway for leveraging quantum computing to enhance classical models without real-time quantum inference latency.