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QSA-QConvLSTM: A Quantum Computing-Based Approach for Spatiotemporal Sequence Prediction

Wenbin Yu, Zongyuan Chen, Chengjun Zhang, Yadang Chen

Published Mar 6, 2025• 3 citations
Publisher

Abstract

The ability to capture long-distance dependencies is critical for improving the prediction accuracy of spatiotemporal prediction models. Traditional ConvLSTM models face inherent limitations in this regard, along with the challenge of information decay, which negatively impacts prediction performance. To address these issues, this paper proposes a QSA-QConvLSTM model, which integrates quantum convolution circuits and quantum self-attention mechanisms. The quantum self-attention mechanism maps query, key, and value vectors using variational quantum circuits, effectively enhancing the ability to model long-distance dependencies in spatiotemporal data. Additionally, the use of quantum convolution circuits improves the extraction of spatial features. Experiments on the Moving MNIST dataset demonstrate the superiority of the QSA-QConvLSTM model over existing models, including ConvLSTM, TrajGRU, PredRNN, and PredRNN v2, with MSE and SSIM scores of 44.3 and 0.906, respectively. Ablation studies further verify the effectiveness and necessity of the quantum convolution circuits and quantum self-attention modules, providing an efficient and accurate approach to quantized modeling for spatiotemporal prediction tasks.

DOI
10.3390/info16030206

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The ability to capture long-distance dependencies is critical for improving the prediction accuracy of spatiotemporal prediction models. Traditional ConvLSTM models face inherent limitations in this regard, along with the challenge of information decay, which negatively impacts prediction performance. To address these issues, this paper proposes a QSA-QConvLSTM model, which integrates quantum convolution circuits and quantum self-attention mechanisms. The quantum self-attention mechanism maps query, key, and value vectors using variational quantum circuits, effectively enhancing the ability to model long-distance dependencies in spatiotemporal data. Additionally, the use of quantum convolution circuits improves the extraction of spatial features. Experiments on the Moving MNIST dataset demonstrate the superiority of the QSA-QConvLSTM model over existing models, including ConvLSTM, TrajGRU, PredRNN, and PredRNN v2, with MSE and SSIM scores of 44.3 and 0.906, respectively. Ablation studies further verify the effectiveness and necessity of the quantum convolution circuits and quantum self-attention modules, providing an efficient and accurate approach to quantized modeling for spatiotemporal prediction tasks.
In the era of noisy intermediate-scale quantum (NISQ) computing, the synergistic collaboration between quantum and classical computing models has emerged as a promising solution for tackling complex computational challenges. Long short-term memory (LSTM), as a popular network for modeling sequential data, has been widely acknowledged for its effectiveness. However, with the increasing demand for data and spatial feature extraction, the training cost of LSTM exhibits exponential growth. In this study, we propose the quantum convolutional long short-term memory (QConvLSTM) model. By ingeniously integrating classical convolutional LSTM (ConvLSTM) networks and quantum variational algorithms, we leverage the variational quantum properties and the accelerating characteristics of quantum states to optimize the model training process. Experimental validation demonstrates that, compared to various LSTM variants, our proposed QConvLSTM model outperforms in terms of performance. Additionally, we adopt a hierarchical tree-like circuit design philosophy to enhance the model’s parallel computing capabilities while reducing dependence on quantum bit counts and circuit depth. Moreover, the inherent noise resilience in variational quantum algorithms makes this model more suitable for spatiotemporal sequence modeling tasks on NISQ devices.
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.
Modeling long-range dependencies in sequential data remains a central challenge in machine learning. Transformers address this challenge through attention mechanisms, but their quadratic complexity with respect to sequence length limits scalability to long contexts. State-space models (SSMs) provide an efficient alternative with linear-time computation by evolving a latent state through recurrent updates, but their memory is typically formed via additive or linear transitions, which can limit their ability to capture complex global interactions across tokens. In this work, we introduce one of the first studies to leverage the superposition property of quantum systems to enhance state-based sequence modeling. In particular, we propose Quantum Long-Attention Memory (QLAM), a hybrid quantum-classical memory mechanism that can be viewed as a quantum extension of state-space models. Instead of maintaining a classical latent state updated through additive dynamics, QLAM represents the hidden state as a quantum state whose amplitudes encode a superposition of historical information. The state evolves through parameterized quantum circuits conditioned on the input, enabling a non-classical, globally update mechanism. In this way, QLAM preserves the recurrent and linear-time structure of SSMs while fundamentally enriching the memory representation through quantum superposition. Unlike attention mechanisms that explicitly compute pairwise interactions, QLAM implicitly captures global dependencies through the evolution of the quantum state, and retrieves task-relevant information via query-dependent measurements. We evaluate QLAM on sequential variants of standard image classification benchmarks, including sMNIST, sFashion-MNIST, and sCIFAR-10, where images are flattened into token sequences. Across all tasks, QLAM consistently improves over recurrent baselines and transformer-based models.
This study proposes a novel hybrid prediction model (QGCN-LSTM) that combines Quantum Graph Convolutional Networks (QGCN) with classical Long Short-Term Memory (LSTM). The model takes space-time data as input and achieves quantum information conversion through a quantum encoding layer. Multi-scale features are extracted through the collaborative computation of QGCN and quantum gated loop units, and a quantum attention module is introduced to dynamically screen key information. Finally, the prediction results are generated through quantum measurement and a classical output layer. In the space-time data prediction task of urban traffic flow, a benchmark model system covering classical, cutting-edge, and traditional architectures was constructed. The experimental results show that QGCN-LSTM utilizes quantum entanglement gates to establish non-local road network associations, dynamically allocate feature weights to enhance the impact of critical time steps, and achieves deep compression of lines through quantum line pruning technology, effectively alleviating the common problem of “poor plateau” in quantum neural network training. In terms of prediction accuracy, the average absolute error (MAE) of its key hub nodes is reduced by 34.1% compared to the graph convolution LSTM (GCN-LSTM) model, and the Spatial Correlation Index (SCI) is improved to 0.89. In addition, it also shows excellent performance in dynamic response, edge computing efficiency, and other aspects, meeting the real-time requirements of the traffic signal control system. This study provides an effective paradigm for the application of quantum collaborative architecture in complex spatiotemporal prediction tasks.
The integration of quantum computing and machine learning has led to innovative algorithms in quantum machine learning that outperform traditional methods in time series forecasting. This paper introduces the Quantum Amplitude-Phase Dropout Attention Model (QAPDAM), which combines Amplitude-Phase Decomposition (APDM) measurement and quantum dropout attention to improve prediction accuracy and robustness while minimizing circuit parameters. The QAPDAM model consists of a Variational Quantum Circuit (VQC) for predictions and an APDM-based dropout self-attention module for feature extraction. Data is encoded into quantum states and processed with a parameter-efficient APDM self-attention mechanism to calculate query, key, and value. Quantum dropout is applied to adjust attention weights dynamically, reducing overfitting and adapting to data variability. Forecasts are obtained through circuit evolution and measurement. We tested QAPDAM's performance in Electric Transformer Temperature dataset, finding it surpasses other models in terms of predictive accuracy with a 25% reduction in circuit parameters.
Attention mechanisms have revolutionized natural language processing. Combining them with quantum computing aims to further advance this technology. This paper introduces a novel Quantum Mixed-State Self-Attention Network (QMSAN) for natural language processing tasks. Our model leverages quantum computing principles to enhance the effectiveness of self-attention mechanisms. QMSAN uses a quantum attention mechanism based on mixed state, allowing for direct similarity estimation between queries and keys in the quantum domain. This approach leads to more effective attention coefficient calculations. We also propose an innovative quantum positional encoding scheme, implemented through fixed quantum gates within the circuit, improving the model's ability to capture sequence information without additional qubit resources. In numerical experiments of text classification tasks on public datasets, QMSAN outperforms Quantum Self-Attention Neural Network (QSANN). Furthermore, we demonstrate QMSAN's robustness in different quantum noise environments, highlighting its potential for near-term quantum devices.