Recurrent neural networks are a kind of recursion which takes sequence data as input and carries on the evolution of temporal dependency data. Variational quantum algorithms use classical computers as the quantum optimizer to update the circuit parameters. In this work, we propose a variational quantum algorithm of the recurrent neural network, which we dub VQRNN, to find approximate optima in the time series forecasting. Motivated by the variational quantum algorithms, we train classical activation functions to assist quantum computing. Here, unlike the quantum tensor networks (QTN) algorithm that predicts a single output feature with a single time step, our algorithm can forecast multi-output features by adjusting the recurrent hidden state. Finally, we deploy the QTN and VQRNN algorithms on the Origin Quantum platform with the numerical simulator backends using the Meteorological data set. Experimental results show that the atmospheric pressure prediction accuracy of VQRNN is 99.8864% in multi-feature forecasting tasks. In addition, we conclude that the variation-based model has an excellent performance in multi-feature output forecasting.
Recurrent neural networks are a kind of recursion which takes sequence data as input and carries on the evolution of temporal dependency data. Variational quantum algorithms use classical computers as the quantum optimizer to update the circuit parameters. In this work, we propose a variational quantum algorithm of the recurrent neural network, which we dub VQRNN, to find approximate optima in the time series forecasting. Motivated by the variational quantum algorithms, we train classical activation functions to assist quantum computing. Here, unlike the quantum tensor networks (QTN) algorithm that predicts a single output feature with a single time step, our algorithm can forecast multi-output features by adjusting the recurrent hidden state. Finally, we deploy the QTN and VQRNN algorithms on the Origin Quantum platform with the numerical simulator backends using the Meteorological data set. Experimental results show that the atmospheric pressure prediction accuracy of VQRNN is 99.8864% in multi-feature forecasting tasks. In addition, we conclude that the variation-based model has an excellent performance in multi-feature output forecasting.
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.
Accurate load forecasting is critical for effective energy management, infrastructure planning, and ensuring the stability of modern power systems. With growing interest in Quantum Computing (QC), recent efforts have demonstrated the applicability of Quantum Machine Learning (QML) across various domains, including supervised and unsupervised learning. However, the use of QML models for Time Series Forecasting (TSF) remains relatively underexplored. In this work, we present a complete framework for TSF based on Variational Quantum Algorithms (VQAs), capable of both single-step and multi-step ahead forecasting. We use tensor product encoding to encode the classical input samples into quantum states, and use the data re-uploading strategy to introduce temporal dependencies across each layer of the quantum circuit. Within this framework, we systematically evaluate multiple Variational Quantum Circuit (VQC) architectures to assess their suitability for forecasting problem. Among the tested configurations, thenLocaland its modified variantQuReUpconsistently outperformed other quantum ansatz designs. Notably, in recursive multi-step forecasting scenarios, these models not only matched but surpassed the performance of a classical Artificial Neural Network (ANN). For example, thenLocalmodel achieved a 8% reduction in mean absolute error (MAE) over ANN for a 24-hour horizon. These results underscore the potential of VQAs for efficient and accurate TSF, particularly in scenarios requiring short to medium-term predictions. The proposed framework offers a promising foundation for future research, including extensions to diverse datasets and deployment on real quantum hardware to study the impact of quantum noise and scalability.
Continuous Variable-based Quantum Computing (CVQC) has been developing at speed with a lot of promise in the field of quantum machine learning. It provides a direct and natural way to accommodate continuous values into the quantum computing framework. We carried out experiments on quantum simulators where we compared the results of time series forecasting on a type of continuous-variable quantum variational circuit, called CV-Quantum Neural Networks (CVQNN) for different types of time series like Energy Consumption data and stock price data. We compared their performance with a discrete variable-based variational quantum algorithm as well as with a classical Neural Network. Experiments showed that CVQNN can function just like a neural network but with a lesser number of parameters while tackling the two obstacles that are faced in qubit-based computing, which are, tackling continuous values and introducing controlled non-linearity into the circuits. We used the circuit for multi-step forecasting that performed better for a larger prediction window than one-step forecasting done iteratively on the predicted data. The resembling architecture of CVQNN with that of a neural network offers the flexibility of using a similar structure for both one-step and multi-step forecasting.
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.
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.