We introduce a lightweight Quantum Prototypical Recurrent Unit (QPRU) that requires significantly fewer parameters than both classical recurrent architectures, such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), and quantum variants, including Quantum LSTM (QLSTM) and Quantum GRU (QGRU). Despite its compact design, the QPRU achieves competitive forecasting performance, matching state-of-the-art baselines while offering important structural and practical advantages, including enhanced scalability and a reduced number of trainable parameters.
We introduce a lightweight Quantum Prototypical Recurrent Unit (QPRU) that requires significantly fewer parameters than both classical recurrent architectures, such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU), and quantum variants, including Quantum LSTM (QLSTM) and Quantum GRU (QGRU). Despite its compact design, the QPRU achieves competitive forecasting performance, matching state-of-the-art baselines while offering important structural and practical advantages, including enhanced scalability and a reduced number of trainable parameters.
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.
Quantum Recurrent Neural Networks are gaining attention for their generalization capability in time series analysis. However, their performance are hindered by lengthy training times and non-scalability. This paper proposes a novel appli- cation for hybrid Quantum Gated Recurrent Units (QGRUs) focused on multivariate time-series forecasting. Our study demonstrates that these architectures outperform classical benchmarks. Through extensive innovative experiments and simulations, our results showcase the versatility and superiority of the hybrid approach, extending the capabilities of QGRUs especially in multidimensional data applications. In addition, the architecture at the basis of the QGRU has 25% fewer quantum parameters than existing Quantum Long Short-Term Memory models, and it is about 25% faster during training and inference stages, leading to feasible implemen- tations on both simulated and real quantum hardware.
Abstract Quantum Recurrent Neural Networks are receiving an increased attention thanks to their enhanced generalization capabilities in time series analysis. However, their performances were bottlenecked by long training times and unscalable architectures. In this paper, we propose a novel Quantum Recurrent Neural Network model based on Quantum Gated Recurrent Units. It uses a learnable Variational Quantum Layer to process temporal data, interspersed with two classical layers to properly match the dimensionality of the input and output vectors. Such an architecture has fewer quantum parameters than existing Quantum Long Short-Term Memory models. Both the quantum networks were evaluated on periodic and real-world time series datasets, together with the classical counterparts. The quantum models exhibited superior performances compared to the classical ones in all the test cases. The Quantum Gated Recurrent Units outperformed the Quantum Long Short-Term Memory network despite having a simpler internal configuration. Moreover, the Quantum Gated Recurrent Units network demonstrated to be about 25% faster during the training and inference procedure over the Quantum Long Short-Term Memory. This improvement in speed comes with one less quantum circuit to be executed, suggesting that our model may offer a more efficient alternative for implementing Quantum Recurrent Neural Networks on both simulated and real quantum hardware.
The rapid growth of modern machine learning (ML) models presents fundamental challenges in parameter efficiency and computational resource requirements. This study introduces the Quantum Recurrent Unit (QRU), a novel quantum neural network (NN) architecture specifically designed to address these challenges while remaining compatible with Noisy Intermediate-Scale Quantum (NISQ) devices. QRU leverages quantum controlled-SWAP (C-SWAP; Fredkin) gates to implement an information selection mechanism inspired by classical Gated Recurrent Units (GRUs), enabling selective processing of temporal information via quantum operations. Through its innovative recurrent architecture featuring measurement results feedforward state propagation and shared parameters across time steps, QRU achieves constant circuit depth and constant parameter count regardless of input sequence length, effectively circumventing stringent NISQ hardware constraints. We systematically validate QRU through three progressive experiments: (1) oscillatory behavior prediction, where 72-parameter QRU matches 197-parameter classical GRU performance; (2) Wisconsin Diagnostic Breast Cancer classification, where 35 parameters achieve 96.13% accuracy comparable to 167-parameter artificial NNs; and (3) MNIST handwritten digit recognition, where 132 parameters reach 98.05% accuracy, outperforming a 27,265-parameter convolutional NN. These results demonstrate that QRU consistently achieves comparable or superior performance with significantly fewer parameters than classical NNs while maintaining constant quantum circuit depth. The architecture's quantum-native design, combining C-SWAP-based information selection with novel recurrent processing, suggests QRU's potential as a fundamental building block for next-generation ML systems, offering a promising pathway toward more efficient and scalable quantum ML architectures.
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.
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.