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Journal of Physics Communications

A variational approach to quantum gated recurrent units

Andrea Ceschini, Antonello Rosato, Massimo Panella

Published Aug 1, 2024• 10 citations
Publisher

Abstract

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.

DOI
10.1088/2399-6528/ad6db7

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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.
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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.
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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.