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Quantum Recurrent Neural Networks for Multivariate Time Series Prediction

Manuel Lagos Rodríguez, Hilda Romero Velo, Álvaro Leitao, Javier Pereira Loureiro, Manuel Francisco González Penedo

Published May 14, 2026• 0 citations
Publisher

Abstract

Classical models for time series forecasting, despite their success, often face challenges related to training, generalization, energy consumption and interpretability. Unconventional computing paradigms, such as quantum computing, offer a promising avenue to address these limitations. Quantum Recurrent Neural Networks (QRNN) emerge as a powerful approach for multivariate time series prediction. Due to some features, the QRNN model we study is not supported in many quantum computers. We develop a specific-purpose emulator to address this barrier, and then we benchmark the model against datasets of varying complexities, involving realistic features such as noisy outputs. The results show significant performance compared to other well-known classical approaches for time series prediction.

DOI
10.17979/spu.23.c57

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Classical models for time series forecasting, despite their success, often face challenges related to training, generalization, energy consumption and interpretability. Unconventional computing paradigms, such as quantum computing, offer a promising avenue to address these limitations. Quantum Recurrent Neural Networks (QRNN) emerge as a powerful approach for multivariate time series prediction. Due to some features, the QRNN model we study is not supported in many quantum computers. We develop a specific-purpose emulator to address this barrier, and then we benchmark the model against datasets of varying complexities, involving realistic features such as noisy outputs. The results show significant performance compared to other well-known classical approaches for time series prediction.
The analysis of historical data allows the execution of predictive tasks such as weather and stock price forecasting. To achieve these goals, Recurrent Neural Networks are implemented in classical computers and, in recent years, quantum methods have also emerged to perform prediction tasks based on the analysis of historical series, which have been called Quantum Recurrent Neural Network (QRNN). The objective of this work is to identify and review the main QRNNs discussed in the literature. A literature search in google scholar resulted in eight relevant papers that were reviewed. In general, the QRNNs show better training accuracy and stability compared to classical methods. It is not possible to speak of a training time advantage with the noisy and low-scale quantum computers currently available.
Abstract Quantum recurrent neural networks (QRNNs) are robust candidates for modelling and predicting future values in multivariate time series. However, the effective implementation of some QRNN models is limited by the need for mid-circuit measurements. Those increase the requirements for quantum hardware, which in the current noisy intermediate-scale quantum era does not allow reliable computations. Emulation arises as the main near-term alternative to explore the potential of QRNNs, but existing quantum emulators are not dedicated to circuits with multiple intermediate measurements. In this context, we design a specific emulation method that relies on density matrix formalism. Using a compact tensor notation, we provide the mathematical formulation of the operator-sum representation involved. This allows us to show how the present and past information from a time series is transmitted through the circuit, and how to reduce the computational cost in every time step of the emulated network. In addition, we derive the analytical gradient and the Hessian of the network outputs with respect to its trainable parameters, which are needed when the outputs have stochastic noise due to hardware errors and a finite number of circuit shots (sampling). We finally test the presented methods using a hardware-efficient ansatz and four diverse datasets that include univariate and multivariate time series, with and without sampling noise. In addition, we compare the model with other existing quantum and classical approaches. Our results show how QRNNs can be trained with numerical and analytical gradients to make accurate predictions of future values by capturing non-trivial patterns of input series with different complexities.
Quantum neural network (QNN) is one of the promising areas in which noisy medium-scale quantum devices (MCD) can find advantageous applications in the short term compared to classical resources. Recurrent neural networks are the most fundamental networks for sequential learning, but there is still no canonical model of a quantum recurrent neural network (QRNN), which certainly limits research in the field of quantum deep learning. In the present paper, a new type of QRNS is proposed that would be a good candidate as a canonical QRNN model, where quantum recurrent blocks (QRB) are built in a hardware-efficient way, and QRNN are constructed by stacking QRB in a checkerboard pattern, which can significantly reduce the algorithm’s requirements with respect to coherent time of quantum devices. That is, QRNN is much more accessible on MCD devices. Numerical experiments show that our QRNN provides much better performance in prediction (classification) accuracy compared to classical RNN and state-of-the-art QNN models for sequential training and can predict changing details of time series data.
Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we approach sequential modeling by applying a reservoir computing (RC) framework to quantum recurrent neural networks (QRNN-RC) that are based on classical RNN, LSTM and GRU. The main idea to this RC approach is that the QRNN with randomly initialized weights is treated as a dynamical system and only the final classical linear layer is trained. Our numerical simulations show that the QRNN-RC can reach results comparable to fully trained QRNN models for several function approximation and time series prediction tasks. Since the QRNN training complexity is significantly reduced, the proposed model trains notably faster. In this work we also compare to corresponding classical RNN-based RC implementations and show that the quantum version learns faster by requiring fewer training epochs in most cases. Our results demonstrate a new possibility to utilize quantum neural network for sequential modeling with greater quantum hardware efficiency, an important design consideration for noisy intermediate-scale quantum (NISQ) computers.
Abstract Modeling temporal dependencies within quantum systems remains a key challenge for quantum machine learning. Current quantum neural networks largely depend on classical recurrent modules, which introduce optimization bottlenecks and coherence loss during sequence processing. To address this, we propose a fully quantum-native recurrent neural network (QRNN) for end-to-end sequential learning. Our architecture captures temporal dynamics through coherent unitary operations, avoiding external classical recurrence and mid-circuit state collapse. The proposed model was benchmarked against a classical recurrent neural network (RNN), quantum tensor networks, and state-of-the-art hybrid QRNN using the Origin Quantum superconducting platform. Experimental evaluations on nonlinear functions, complex dynamical systems, and meteorological datasets demonstrate that our quantum-native QRNN achieves improved prediction accuracy and exhibits enhanced capability in forecasting complex temporal features. For instance, on the relative humidity forecasting task, the proposed QRNN achieves a 73.5% reduction in Root mean square error compared to the hybrid VQRNN. This work establishes a robust framework for preserving coherence in pure quantum sequential processing, offering a scalable path for time-series forecasting on near-term quantum hardware.
This paper is a survey on the use of fully-quantum digital recurrent neural networks (QRNNs) for time-series forecasting with real-world data. It discusses precedent QRNN papers, their methodology and evaluation strategies, and highlights that, despite their intuitive applicability to the problem, QRNNs haven't been rigorously evaluated with forecasting tasks. Finally, it presents some real-data forecasting experiment results and a couple examples of how experiment setup can affect the outcomes. These results serve to inform and motivate future work, with the goal of useful QRNN prediction.