This paper aims at solving time series prediction problems by means of a hybrid quantum-classical recurrent neural network. We propose a novel architecture based on stacked Long Short-Term Memory layers and a variational quantum layer. The latter employs a quantum feature map to embed input data into quantum states, which are then processed by a circuit ansatz. Finally, the expectation value of the circuit's outcome is taken over Pauli observables. Quantum properties such as superposition and entanglement are exploited to perform computations efficiently in a high-dimensional feature space. The proposed hybrid quantum-classical neural network is applied to a real-life challenging problem pertaining to the prediction of renewable energy time series. The comparison between the proposed approach and the classical counterpart shows that the former achieves better results in terms of prediction error, thus demonstrating better approximation of stochastic fluctuations and an overall effectiveness of the quantum variational approach also for prediction tasks.
This paper aims at solving time series prediction problems by means of a hybrid quantum-classical recurrent neural network. We propose a novel architecture based on stacked Long Short-Term Memory layers and a variational quantum layer. The latter employs a quantum feature map to embed input data into quantum states, which are then processed by a circuit ansatz. Finally, the expectation value of the circuit's outcome is taken over Pauli observables. Quantum properties such as superposition and entanglement are exploited to perform computations efficiently in a high-dimensional feature space. The proposed hybrid quantum-classical neural network is applied to a real-life challenging problem pertaining to the prediction of renewable energy time series. The comparison between the proposed approach and the classical counterpart shows that the former achieves better results in terms of prediction error, thus demonstrating better approximation of stochastic fluctuations and an overall effectiveness of the quantum variational approach also for prediction tasks.
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.
Prediction of stock price remains a challenging task because financial markets are dynamic and often non-linear, unpredictable patterns. To deal with such unpredictable data, the architecture that’s created must identify both time based trends and hidden patterns in data. In this study, we explore a hybrid modelling approach by combining both the classical deep learning techniques with quantum computing principles. Specifically, a Long Short-Term Memory (LSTM) is combined with a Quantum Neural Network (QNN) to understand the benefits of using quantum in time series forecasting. Rather than depending on a single quantum configuration, multiple feature maps and ansatz circuit designs were evaluated to identify the most suitable arrangement for the QLSTM model. Resultant framework blends ideas from both classical computing and quantum approaches to improve how we predict patterns over time in real-life scenarios.
Time series forecasting is vital in many fields, including energy demand prediction and financial markets. Long Short-Term Memory (LSTM) networks have demonstrated strong performance in capturing temporal dependencies in sequential data. However, traditional LSTM face challenges such as vanishing gradients and limited capabilities in modeling long-term dependencies, especially with complex, high-dimensional data. The model integrates Variable Quantum Circuit (VQC) into a modified LSTM (mLSTM) structure, taking advantage of quantum properties such as superposition and entanglement to improve memory retention and computational efficiency. We would like to introduce modified Quantum Long Short-Term Memory (mQLSTM), which is specifically designed for photovoltaic (PV) energy forecasting. Key improvements include a quantum memory mechanism that mitigates loss of information over extended sequences, a redesigned forget gate to enhance long-term learning and an Exponentially Weighted Feature (EWF) layer to accelerate convergence and enhance generalization. This paper highlights the potential of quantum-enhanced deep learning architectures to advance time series forecasting and opens new directions for practical applications in renewable energy and beyond.
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.
Long short-term memory (LSTM) is a kind of recurrent neural networks (RNN) for sequence and temporal dependency data modeling and its effectiveness has been extensively established. In this work, we propose a hybrid quantum-classical model of LSTM, which we dub QLSTM. We demonstrate that the proposed model successfully learns several kinds of temporal data. In particular, we show that for certain testing cases, this quantum version of LSTM converges faster, or equivalently, reaches a better accuracy, than its classical counterpart. Due to the variational nature of our approach, the requirements on qubit counts and circuit depth are eased, and our work thus paves the way toward implementing machine learning algorithms for sequence modeling such as natural language processing, speech recognition on noisy intermediate-scale quantum (NISQ) devices.
We present a hybrid quantum-classical recurrent neural network (QRNN) architecture in which the recurrent core is realized as a parametrized quantum circuit (PQC) controlled by a classical feedforward network. The hidden state is the quantum state of an n-qubit PQC in an exponentially large Hilbert space C2n, which serves as a coherent recurrent quantum memory. The PQC is unitary by construction, making the hidden-state evolution norm-preserving without external constraints. At each timestep, mid-circuit Pauli expectation-value readouts are combined with the input embedding and processed by the feedforward network, which provides explicit classical nonlinearity. The outputs parametrize the PQC, which updates the hidden state via unitary dynamics. The QRNN is compact and physically consistent, and it unifies (i) unitary recurrence as a high-capacity memory, (ii) partial observation via mid-circuit readouts, and (iii) nonlinear classical control for input-conditioned parametrization. We evaluate the model in simulation with up to 14 qubits on sentiment analysis, MNIST, permuted MNIST, copying memory, and language modeling. For sequence-to-sequence learning, we further devise a soft attention mechanism over the mid-circuit readouts and show its effectiveness for machine translation. To our knowledge, this is the first model (RNN or otherwise) grounded in quantum operations to achieve competitive performance against strong classical baselines across a broad class of sequence-learning tasks.