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.
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.
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.
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.
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.
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.
Quantum neural networks have emerged as promising quantum machine learning models, leveraging the properties of quantum systems and classical optimization to solve complex problems in physics and beyond. However, previous studies have demonstrated inevitable trainability issues that severely limit their capabilities in the large-scale regime. In this work, we propose a quantum recurrent embedding neural network (QRENN) inspired by fast-track information pathways in ResNet and general quantum circuit architectures in quantum information theory. By employing dynamical Lie algebras, we provide a rigorous proof of the trainability of QRENN circuits, demonstrating that this deep quantum neural network can avoid barren plateaus. Notably, the general QRENN architecture resists classical simulation as it encompasses powerful quantum circuits such as QSP, QSVT, and DQC1, which are widely believed to be classically intractable. Building on this theoretical foundation, we apply our QRENN to accurately classify quantum Hamiltonians and detect symmetry-protected topological phases, demonstrating its applicability in quantum supervised learning. Our results highlight the power of recurrent data embedding in quantum neural networks and the potential for scalable quantum supervised learning in predicting physical properties and solving complex problems.