Hybrid Classical–Quantum Surrogate Modeling for Nonlinear Reactor Dynamics: A Comparative Study of GRU, LSTM, Transformer, and Variational Quantum Circuits
This preprint presents a comparative study of classical recurrent neural networks and hybrid quantum-classical models for surrogate modeling of nonlinear dynamical systems. A synthetic reactor dataset exhibiting coupled multi-frequency behavior is used to evaluate GRU, LSTM, Transformer, and Variational Quantum Circuit (VQC) architectures under identical training conditions. Model performance is assessed using RMSE, MAE, and R² metrics. Results show that recurrent architectures outperform both Transformer and VQC approaches on this task, highlighting the effectiveness of memory-based models for nonlinear time-series prediction and the current limitations of near-term quantum machine learning methods in complex regression settings. The study provides insights into the applicability of hybrid quantum-classical approaches for scientific surrogate modeling and time-series forecasting.
This preprint presents a comparative study of classical recurrent neural networks and hybrid quantum-classical models for surrogate modeling of nonlinear dynamical systems. A synthetic reactor dataset exhibiting coupled multi-frequency behavior is used to evaluate GRU, LSTM, Transformer, and Variational Quantum Circuit (VQC) architectures under identical training conditions. Model performance is assessed using RMSE, MAE, and R² metrics. Results show that recurrent architectures outperform both Transformer and VQC approaches on this task, highlighting the effectiveness of memory-based models for nonlinear time-series prediction and the current limitations of near-term quantum machine learning methods in complex regression settings. The study provides insights into the applicability of hybrid quantum-classical approaches for scientific surrogate modeling and time-series forecasting.
In this study, we investigate Quantum Long Short-Term Memory and Quantum Gated Recurrent Unit integrated with Variational Quantum Circuits in modeling complex dynamical systems, including the Van der Pol oscillator, coupled oscillators, and the Lorenz system. We implement these advanced quantum machine learning techniques and compare their performance with traditional Long Short-Term Memory and Gated Recurrent Unit models. The results of our study reveal that the quantum-based models deliver superior precision and more stable loss metrics throughout 100 epochs for both the Van der Pol oscillator and coupled harmonic oscillators, and 20 epochs for the Lorenz system. The Quantum Gated Recurrent Unit outperforms competing models, showcasing notable performance metrics. For the Van der Pol oscillator, it reports MAE 0.0902 and RMSE 0.1031 for variable x and MAE 0.1500 and RMSE 0.1943 for y; for coupled oscillators, Oscillator 1 shows MAE 0.2411 and RMSE 0.2701 and Oscillator 2 MAE is 0.0482 and RMSE 0.0602; and for the Lorenz system, the results are MAE 0.4864 and RMSE 0.4971 for x, MAE 0.4723 and RMSE 0.4846 for y, and MAE 0.4555 and RMSE 0.4745 for z. These outcomes mark a significant advancement in the field of quantum machine learning.
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.
Abstract Sarcasm detection is a challenging task in Natural Language Processing (NLP) due to its reliance on subtle and implicit linguistic cues that are often not explicitly expressed in text. Designing models capable of capturing such nuanced patterns remains an open problem. In this work, we investigate hybrid quantum–classical recurrent architectures for sarcasm detection by conducting a comparative study of classical and quantum-enhanced sequence models, including Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and their quantum counterparts, Quantum LSTM (QLSTM) and Quantum GRU (QGRU).We employ a pre-trained BERT model to extract contextualized token embeddings, which are subsequently compressed through classical neural layers to ensure compatibility with Noisy Intermediate-Scale Quantum (NISQ) devices. In the proposed quantum-enhanced models, classical linear transformations within recurrent gates are replaced by Variational Quantum Circuits (VQCs), enabling the exploitation of quantum properties such as superposition and entanglement within a hybrid learning framework.Experimental results on a balanced sarcasm-labeled dataset indicate that both QLSTM and QGRU achieve performance levels comparable to their classical counterparts, despite utilizing significantly fewer trainable parameters. Notably, the quantum-enhanced models require approximately 10% of the parameters used by their classical equivalents while maintaining similar macro F1 scores. These findings suggest that hybrid quantum recurrent architectures can serve as compact and parameter-efficient alternatives to classical sequence models, highlighting their potential applicability in quantum natural language processing under near-term hardware constraints.
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.
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.
Variational quantum circuits (VQCs) have been proposed as promising models for nonlinear learning tasks in the noisy intermediate-scale quantum (NISQ) era. This study presents a hybrid classical-quantum framework for nonlinear time-series forecasting that integrates causally-filtered Hidden Markov regime detection with multiple VQC architectures. Four circuit architectures are defined as an explicit [Formula: see text] factorial design that isolates circuit depth from entanglement topology (shallow: depth 1/linear; ring: depth 1/ring; deep: depth 4/linear; heavy: depth 4/ring), each with reported qubit count, parameter count and gate count, and are evaluated under an analytic depolarizing/readout noise model. Three nonlinear classical baselines (support-vector regression, gradient boosting, and a multilayer perceptron) are compared alongside a linear autoregressive (AR) baseline, and the Hidden Markov Model (HMM) regime feature is fit only on training data and propagated causally into the test set to remove look-ahead leakage. Across 20 Monte Carlo replicates, we find that every VQC architecture is outperformed by every classical baseline, including plain linear AR (paired t-tests, all [Formula: see text]; Cohen’s d up to 4.8). Within the VQC family, circuit depth - not shallowness - is associated with better performance (deep/heavy [Formula: see text] shallow/ring), while entanglement topology alone has little independent effect once depth is controlled. An ablation removing the HMM-derived feature shows it contributes negligibly to forecast accuracy in this setting. Under this confound-controlled design, we find no evidence of a forecasting advantage for the tested VQC architectures over classical linear or nonlinear baselines, which we report as a cautionary result for claims of near-term quantum advantage in forecasting.