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.
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.
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.
In this paper, we address the challenge of multivariate time-series forecasting using quantum machine learning techniques. We introduce adaptation strategies that extend variational quantum circuit models, traditionally limited to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid architectures to systematically evaluate their capacity to model cross-variable dependencies. Second, building upon these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Third, we provide a comprehensive empirical evaluation on both synthetic and real-world datasets, showing that quantum-based models may achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines in some cases. These contributions highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.
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.
Long short-term memory (LSTM) is a widely used artificial neural network that is well suited for time series prediction. Quantum machine learning as a new research topic combines the advantages of quantum data processing and classical machine learning. In this paper, based on a hybrid quantum classical scheme, we design a quantum enhanced LSTM model and several variants such as QGRU. We also performed experiments with a multivariate time series prediction problem to verify the feasibility of these models. Through this research, we expect to explore the benefits and implementation of quantum-based machine learning.
Abstract In this paper, we address the challenge of multivariate time-series forecasting through quantum-enhanced machine learning architectures. We propose adaptation strategies that extend variational quantum circuit models (VQC), traditionally constrained to univariate data, toward the multivariate setting, exploring both purely quantum and hybrid quantum-classical formulations. First, we extend and benchmark several VQC-based and hybrid models to systematically evaluate their ability to capture cross-variable dependencies. Building on these foundations, we introduce the iQTransformer, a novel quantum transformer architecture that integrates a quantum self-attention mechanism within the iTransformer framework, enabling a quantum-native representation of inter-variable relationships. Finally, we present a comprehensive empirical evaluation on both synthetic and real-world datasets, demonstrating that quantum-enhanced models can achieve competitive or superior forecasting accuracy with fewer trainable parameters and faster convergence than state-of-the-art classical and quantum baselines. These findings highlight the potential of quantum-enhanced architectures as efficient and scalable tools for advancing multivariate time-series forecasting.