Quantum long short-term memory (QLSTM) models extend recurrent sequence learning with variational quantum circuits, but their optimization behavior can vary substantially across random initializations and temporal contexts. This paper evaluates a recursive QLSTM architecture against a standard QLSTM for one-step-ahead prediction of daily minimum and maximum temperature. Using daily weather observations from Toronto and identical training settings, we compare convergence, predictive accuracy, and generalization across input windows of 8, 16, and 32 days over 20 random seeds. The recursive model consistently reaches a near-optimal test loss earlier, reduces mean absolute error and root mean squared error, and exhibits a smaller generalization gap. These results indicate that recursive quantum feature transformations can improve stability and out-of-sample performance for compact hybrid quantum--classical temporal models.
Quantum long short-term memory (QLSTM) models extend recurrent sequence learning with variational quantum circuits, but their optimization behavior can vary substantially across random initializations and temporal contexts. This paper evaluates a recursive QLSTM architecture against a standard QLSTM for one-step-ahead prediction of daily minimum and maximum temperature. Using daily weather observations from Toronto and identical training settings, we compare convergence, predictive accuracy, and generalization across input windows of 8, 16, and 32 days over 20 random seeds. The recursive model consistently reaches a near-optimal test loss earlier, reduces mean absolute error and root mean squared error, and exhibits a smaller generalization gap. These results indicate that recursive quantum feature transformations can improve stability and out-of-sample performance for compact hybrid quantum--classical temporal models.
Forecasting weather is critical in different application sectors and affects decision-making and resource distribution. Long Short-Term Memory (LSTM) models are popular, but they can be improved even further with the use of quantum computing techniques. This paper discusses a Quantum Long Short-Term Memory (QLSTM) simulated in PennyLane-based simulators. According to the experimental results, the suggested QLSTM model produced a mean absolute error (MAE) of 0.009066, a test mean square error (MSE) of 0.000162, and a coefficient of determination (R2) of 0.999846, surpassing both quantum models and classical baselines. These results highlight the potential of quantum-assisted architectures to improve accuracy in weather prediction. The research advances weather forecasting and contributes to quantum computing applications, guiding researchers in developing precise weather prediction models and enhancing decision-making in weather-sensitive domains. The proposed 4-qubit quantum model was tested with noise models, and it demonstrated high learning efficiency and strong robustness against realistic NISQ-level noise, maintaining stable optimization and low error even under moderate perturbations. • Quantum LSTM Development: The classical LSTM was extended into the quantum domain using Variational Quantum Circuits (VQCs) for feature extraction and data compression, applied to weather prediction tasks. • Experimental Evaluation: Three QLSTM variants (4, 6, and 8 qubit) were tested on two weather datasets and compared with classical LSTM and state-of-the-art QLSTM models. • Performance and Robustness: The QLSTM models outperformed baseline models, with the 4-qubit model showing strong learning efficiency and robustness under realistic NISQ-level noise.
Recent advances in quantum computing and machine learning have motivated the development of quantum models for sequential data processing. In this paper, we propose a Recursive Quantum Long Short-Term Memory model, or Recursive QLSTM, which extends QLSTM through metacore-based recursive constructions. We numerically test the model under different input sequence lengths, metacore designs, and recursive rules, and identify the best-performing architecture among these variants. For this selected model, we further provide theoretical arguments explaining why its recursive structure improves temporal information propagation and enhances learning performance. Our results suggest that Recursive QLSTM offers a flexible and effective framework for quantum recurrent learning over input time series of various lengths.
Abstract Hybrid quantum recurrent models are commonly evaluated against compact classical networks, making it diffcult to determine whether observed gains arise from the variational quantum circuit (VQC) or from the surrounding recurrent architecture. This study presents an architecture and parameter-controlled evaluation of quantum gated recurrent unit (QGRU) and quantum long short-term memory (QLSTM) models for one-step-ahead meteorological forecasting. Each quantum model is compared with both a compact, approximately parameter-matched recurrent baseline and an exact classical gate-core surrogate that preserves the hidden width, recurrent equations, gate-specific pre-/post-projections, optimization protocol, and total trainable-parameter count. All models use 17 input features, 24-step histories, a chronological 80/10/10 train–validation–test split, trainingonly standardization, and ten matched random seeds. QGRU achieves an RMSE of 1.1045 ± 0.0693, reducing test RMSE by 19.01% relative to the compact GRU and by 5.47% relative to its exact 773-parameter surrogate. It also attains a lower mean best validation MSE, reaches 95% of its achievable validation improvement after 5.5 ± 0.5 epochs, and exhibits a smaller final train–validation gap. QLSTM reduces test RMSE by 24.80% relative to the compact LSTM, while its exact 1,025-parameter surrogate achieves comparable predictive performance with slightly greater validation stability. Analysis of 1,949 epoch-level records across convergence, checkpoint quality, early stopping, generalization, and runtime demonstrates that VQC utility depends on the recurrent architecture in which it is embedded. All experiments are conducted using ideal noiseless statevector simulation.
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.
Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling on noisy intermediate-scale quantum (NISQ) devices.
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.