International Journal of Computer Information Systems and Industrial Management Applications
A Hybrid Quantum Neural Network for Closing-Stock Price Forecasting: Variational Circuits, Temporal Memory, and Attention with a Theoretical Account of Expressivity, Trainability, and Scaling
Predicting the closing price of an equity remains stubbornly hard: price series are noisy, non-stationary, and shaped by feedback that breaks the assumptions of linear models. We revisit the problem with a hybrid quantum neural network (HQNN) that places a small variational quantum circuit (VQC) in front of a recurrent–attention forecaster, and — going beyond an empirical demonstration — we supply a theoretical account of why such a model is expressive, trainable, and computationally lean. The architecture works in two coupled stages. A four-qubit VQC first maps an amplitude-encoded feature vector through parameterised / rotations and CNOT–CZ entangling gates, with exact gradients supplied by the parameter-shift rule; the resulting expectation values form a compact quantum latent code. A stacked Long Short-Term Memory (LSTM) network with eight-head self-attention then resolves the temporal structure of that code over a sixty-day look-back window. On the evaluation data the model reaches a root-mean-square error (RMSE) of 1.74 USD, a mean absolute error (MAE) of 1.42 USD, and a coefficient of determination , ahead of a standalone LSTM (RMSE 3.45), a DCQ-GA Elman network (4.82), a blind-quantum-computing QNN (5.13), and a variational QNN–LSTM (3.97). An ablation isolates each component and shows that removing the quantum stage is by far the most damaging single change, cutting accuracy from 98.26% to 93.41%. Our theoretical contribution interprets the VQC as a truncated Fourier model whose accessible spectrum is set by the encoding depth, shows that the shallow four-qubit design sits well clear of the barren-plateau regime, recasts the circuit’s KL penalty as a quantum information bottleneck, and derives the sub-linear training-time scaling — about against the LSTM’s near-quadratic growth — that we observe empirically up to 100,000 samples. Together these results position the HQNN as a compact and theoretically motivated forecaster for non-stationary financial series, with downstream value for risk control and capital allocation.
Predicting the closing price of an equity remains stubbornly hard: price series are noisy, non-stationary, and shaped by feedback that breaks the assumptions of linear models. We revisit the problem with a hybrid quantum neural network (HQNN) that places a small variational quantum circuit (VQC) in front of a recurrent–attention forecaster, and — going beyond an empirical demonstration — we supply a theoretical account of why such a model is expressive, trainable, and computationally lean. The architecture works in two coupled stages. A four-qubit VQC first maps an amplitude-encoded feature vector through parameterised / rotations and CNOT–CZ entangling gates, with exact gradients supplied by the parameter-shift rule; the resulting expectation values form a compact quantum latent code. A stacked Long Short-Term Memory (LSTM) network with eight-head self-attention then resolves the temporal structure of that code over a sixty-day look-back window. On the evaluation data the model reaches a root-mean-square error (RMSE) of 1.74 USD, a mean absolute error (MAE) of 1.42 USD, and a coefficient of determination , ahead of a standalone LSTM (RMSE 3.45), a DCQ-GA Elman network (4.82), a blind-quantum-computing QNN (5.13), and a variational QNN–LSTM (3.97). An ablation isolates each component and shows that removing the quantum stage is by far the most damaging single change, cutting accuracy from 98.26% to 93.41%. Our theoretical contribution interprets the VQC as a truncated Fourier model whose accessible spectrum is set by the encoding depth, shows that the shallow four-qubit design sits well clear of the barren-plateau regime, recasts the circuit’s KL penalty as a quantum information bottleneck, and derives the sub-linear training-time scaling — about against the LSTM’s near-quadratic growth — that we observe empirically up to 100,000 samples. Together these results position the HQNN as a compact and theoretically motivated forecaster for non-stationary financial series, with downstream value for risk control and capital allocation.
Predicting the closing price of an equity remains stubbornly hard: price series are noisy, non-stationary, and shaped by feedback that breaks the assumptions of linear models. We revisit the problem with a hybrid quantum neural network (HQNN) that places a small variational quantum circuit (VQC) in front of a recurrent–attention forecaster, and — going beyond an empirical demonstration — we supply a theoretical account of why such a model is expressive, trainable, and computationally lean. The architecture works in two coupled stages. A four-qubit VQC first maps an amplitude-encoded feature vector through parameterised R_y/R_z rotations and CNOT–CZ entangling gates, with exact gradients supplied by the parameter-shift rule; the resulting expectation values form a compact quantum latent code. A stacked Long Short-Term Memory (LSTM) network with eight-head self-attention then resolves the temporal structure of that code over a sixty-day look-back window. On the evaluation data the model reaches a root-mean-square error (RMSE) of 1.74 USD, a mean absolute error (MAE) of 1.42 USD, and a coefficient of determination R^2=0.983, ahead of a standalone LSTM (RMSE 3.45), a DCQ-GA Elman network (4.82), a blind-quantum-computing QNN (5.13), and a variational QNN–LSTM (3.97). An ablation isolates each component and shows that removing the quantum stage is by far the most damaging single change, cutting accuracy from 98.26% to 93.41%. Our theoretical contribution interprets the VQC as a truncated Fourier model whose accessible spectrum is set by the encoding depth, shows that the shallow four-qubit design sits well clear of the barren-plateau regime, recasts the circuit’s KL penalty as a quantum information bottleneck, and derives the sub-linear training-time scaling — about O(N^0.62 ) against the LSTM’s near-quadratic growth — that we observe empirically up to 100,000 samples. Together these results position the HQNN as a compact and theoretically motivated forecaster for non-stationary financial series, with downstream value for risk control and capital allocation.
Cryptocurrency price prediction remains a challenging problem due to the highly volatile nature of digital asset markets. This study introduces a Hybrid Quantum-Classical Neural Network (HQCNN) for cryptocurrency price forecasting, leveraging quantum feature encoding and extraction with deep learning architectures. The proposed model utilizes Quantum Convolutional Neural Networks (QCNN) to enhance feature representations, which are then processed by classical deep learning models such as Long Short-Term Memory (LSTM) and Transformer networks. Experimental results on historical cryptocurrency data demonstrate that HQCNN outperforms state-of-the-art models. The proposed model achieves a mean absolute error (MAE) of 0.023 and a root mean squared error (RMSE) of 0.036, surpassing traditional deep learning methods such as LSTM (MAE: 0.040, RMSE: 0.056) and Transformerbased models (MAE: 0.035, RMSE: 0.050). Ablation studies confirm the importance of quantum feature encoding, as removing it degrades performance by up to 38.2%. Additionally, HQCNN reduces inference time to 7 milliseconds, making it suitable for real-time trading applications. Despite its advantages, HQCNN faces challenges related to quantum hardware constraints, training overhead, and interpretability in financial decision-making. Future work will focus on deploying the model on real quantum processors, integrating reinforcement learning for market adaptability, and enhancing interpretability with quantum explainability techniques.
Prediction of stock price remains a challenging task because financial markets are dynamic and often non-linear, unpredictable patterns. To deal with such unpredictable data, the architecture that’s created must identify both time based trends and hidden patterns in data. In this study, we explore a hybrid modelling approach by combining both the classical deep learning techniques with quantum computing principles. Specifically, a Long Short-Term Memory (LSTM) is combined with a Quantum Neural Network (QNN) to understand the benefits of using quantum in time series forecasting. Rather than depending on a single quantum configuration, multiple feature maps and ansatz circuit designs were evaluated to identify the most suitable arrangement for the QLSTM model. Resultant framework blends ideas from both classical computing and quantum approaches to improve how we predict patterns over time in real-life scenarios.
Hybrid quantum-classical recurrent architectures have been proposed for capturing non-stationary, fat-tailed dynamics typical of financial time series, but most published evaluations compare a Quantum Long Short-Term Memory network only against plain Long Short-Term Memory on a single asset. This study contributes a controlled multi-baseline benchmark using four synthetic asset classes generated by calibrated Generalised Autoregressive Conditional Heteroskedasticity processes, comparing six architectures at a matched parameter budget below three hundred and fifty trainable parameters across five random seeds. The comparison set includes Long Short-Term Memory, Bidirectional Long Short-Term Memory, a compact Patch Time Series Transformer, Neural Basis Expansion Analysis, an Inverted Transformer, and a four-qubit Quantum Long Short-Term Memory with two variational blocks. Significance is established through Wilcoxon signed-rank tests, walk-forward validation across three expanding folds, depolarising-noise robustness sweeps, and a variational circuit depth ablation. The principal empirical finding is that compact classical recurrence dominates the benchmark on root mean squared error, while the quantum model exhibits the lowest seed-to-seed variance and the highest directional accuracy on the most volatile asset class.
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.
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.