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Physica Scripta

Quantum gated recurrent neural networks for continuous dynamic temporal decision-making

JiaZhao Shen, Zijun Guo, Wei Ding, Guoliang Shentu, Hongyang Ma

Published Aug 14, 2026• 0 citations
Publisher

Abstract

Abstract Performance breakthroughs in dynamic temporal decision-making tasks have long been a core research objective in reinforcement learning. Yet traditional policy networks, including long short-term memory (LSTM) networks, gated recurrent unit (GRU) and feedforward neural network (FNN), have long been hampered by inherent bottlenecks: low reward efficiency and training instability, which renders them less capable of meeting the high-precision decision-making demands of complex scenarios. This paper introduces a novel policy network, quantum gated recurrent neural network (QGRNN), which incorporates quantum superposition encoding and cyclic entanglement structures to achieve more efficient state-space exploration. Furthermore, the network employs a quantum–classical hybrid residual design that effectively integrates quantum measurement outcomes with classical inputs, thereby strengthening the representational capacity for temporal decision-making features. Trained over 800 episodes via proximal policy optimization in CartPole-v1, the QGRNN achieves an average reward of 380.3 ± 128.6 in the last 100 episodes-significantly outperforming GRU (275.9 ± 140.7), LSTM (239.7 ± 131.8), and FNN (219.2 ± 109.5). As a 4-qubit proof-of-concept, it achieves 45% high-performance episodes (rewards > 450) and demonstrates low-resource, high-performance characteristics for temporal decision-making.

DOI
10.1088/1402-4896/ae99cd

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The exploration of quantum advantages with Quantum Neural Networks (QNNs) is an exciting endeavor. Recurrent neural networks, the widely used framework in deep learning, suffer from the gradient vanishing and exploding problem, which limits their ability to learn long-term dependencies. To address this challenge, in this work, we develop the sequential model of Quantum Gated Recurrent Neural Networks (QGRNNs). This model naturally integrates the gating mechanism into the framework of the variational ansatz circuit of QNNs, enabling efficient execution on near-term quantum devices. We present rigorous proof that QGRNNs can preserve the gradient norm of long-term interactions throughout the recurrent network, enabling efficient learning of long-term dependencies. Meanwhile, the architectural features of QGRNNs can effectively mitigate the barren plateau phenomenon. The effectiveness of QGRNNs in sequential learning is convincingly demonstrated through various typical tasks, including solving the adding problem, learning gene regulatory networks, and predicting stock prices. The hardware-efficient architecture and superior performance of our QGRNNs indicate their promising potential for finding quantum advantageous applications in the near term.
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.
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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.
Quantum reinforcement learning (QRL) has emerged as a framework to solve sequential decision-making tasks, showcasing empirical quantum advantages. A notable development is through quantum recurrent neural networks (QRNNs) for memory-intensive tasks such as partially observable environments. However, QRL models incorporating QRNN encounter challenges such as inefficient training of QRL with QRNN, given that the computation of gradients in QRNN is both computationally expensive and time-consuming. This work presents a novel approach to address this challenge by constructing QRL agents utilizing QRNN-based reservoirs, specifically employing quantum long short-term memory (QLSTM). QLSTM parameters are randomly initialized and fixed without training. The model is trained using the asynchronous advantage actor-critic (A3C) algorithm. Through numerical simulations, we validate the efficacy of our QLSTM-Reservoir RL framework. Its performance is assessed on standard benchmarks, demonstrating comparable results to a fully trained QLSTM RL model with identical architecture and training settings.