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.
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.
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.
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.
Quantum neural network (QNN) is one of the promising directions where the near-term noisy intermediate-scale quantum (NISQ) devices could find advantageous applications against classical resources. Recurrent neural networks are the most fundamental networks for sequential learning, but up to now there is still a lack of canonical model of quantum recurrent neural network (QRNN), which certainly restricts the research in the field of quantum deep learning. In the present work, we propose a new kind of QRNN which would be a good candidate as the canonical QRNN model, where, the quantum recurrent blocks (QRBs) are constructed in the hardware-efficient way, and the QRNN is built by stacking the QRBs in a staggered way that can greatly reduce the algorithm's requirement with regard to the coherent time of quantum devices. That is, our QRNN is much more accessible on NISQ devices. Furthermore, the performance of the present QRNN model is verified concretely using three different kinds of classical sequential data, i.e., meteorological indicators, stock price, and text categorization. The numerical experiments show that our QRNN achieves much better performance in prediction (classification) accuracy against the classical RNN and state-of-the-art QNN models for sequential learning, and can predict the changing details of temporal sequence data. The practical circuit structure and superior performance indicate that the present QRNN is a promising learning model to find quantum advantageous applications in the near term.
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.
Quantum Neural Networks (QNNs) represent a novel computational paradigm that merges the principles of quantum computing with the architecture of artificial neural networks. Through the quantum phenomena of superposition, entanglement, and interference, QNNs enable parallel computation in high-dimensional Hilbert spaces, offering the potential to surpass the representational limits of classical models. This review provides a comprehensive overview of the theoretical foundations and architectures of QNNs, including Quantum Perceptrons, Variational Quantum Circuits (VQCs), Quantum Convolutional Neural Networks (QCNNs), and Quantum Recurrent Neural Networks (QRNNs). Furthermore, it discusses hybrid quantum–classical training mechanisms and key challenges such as barren plateaus, decoherence, and sampling complexity. The review also highlights recent applications of QNNs in medical diagnostics, materials science, and financial forecasting, demonstrating their potential to accelerate computation and improve predictive accuracy. Finally, future research directions are discussed in relation to computational efficiency, model interpretability, and integration with next-generation quantum hardware.
Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning, such as machine translation and speech synthesis. In contrast, applied quantum computing is in its infancy. Nevertheless there already exist quantum machine learning models such as variational quantum eigensolvers which have been used successfully e.g. in the context of energy minimization tasks. In this work we construct a quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks such as sequence learning and integer digit classification. The QRNN cell is built from parametrized quantum neurons, which, in conjunction with amplitude amplification, create a nonlinear activation of polynomials of its inputs and cell state, and allow the extraction of a probability distribution over predicted classes at each step. To study the model's performance, we provide an implementation in pytorch, which allows the relatively efficient optimization of parametrized quantum circuits with thousands of parameters. We establish a QRNN training setup by benchmarking optimization hyperparameters, and analyse suitable network topologies for simple memorisation and sequence prediction tasks from Elman's seminal paper (1990) on temporal structure learning. We then proceed to evaluate the QRNN on MNIST classification, both by feeding the QRNN each image pixel-by-pixel; and by utilising modern data augmentation as preprocessing step. Finally, we analyse to what extent the unitary nature of the network counteracts the vanishing gradient problem that plagues many existing quantum classifiers and classical RNNs.