Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

CG-QRNN: A Conditional Gated Quantum Recurrent Neural Network with Recurrent Temporal Attention

Haibin Wang, Tianjiao Li, Wenjie Liu, Qingshan Wu

Published Oct 8, 2026• 0 citations
Publisher

Abstract

Abstract Quantum recurrent neural networks (QRNNs) have been investigated as a promising paradigm for sequential modeling by integrating parameterized quantum circuits with recurrent architectures. However, existing QRNNs often require additional quantum resources to implement effective gating mechanisms and struggle to capture long-range temporal dependencies. To address these issues, a Conditional Gated Quantum Recurrent Neural Network with Recurrent Temporal Attention (CG-QRNN) is proposed. The Conditional Gating (CG) strategy uses mid-circuit measurement outcomes as control signals to selectively execute subsequent quantum operations within each recurrent update. By coupling intermediate measurement with conditional quantum operations, quantum gating is implemented while the existing qubits are reused, thereby avoiding the introduction of additional qubits for quantum gating. The Recurrent Temporal Attention (RTA) mechanism uses the current hidden state to interact with historical hidden states and dynamically determines their contributions to the current recurrent update. The historical hidden states are then aggregated according to these contributions and incorporated into the current hidden state update. Experiments on five ordinary differential equation benchmarks demonstrate that the CG-QRNN achieves superior overall performance, with average prediction errors reduced by 59.1%, 69.6%, 83.3%, and 97.5% compared with the best-performing baselines on the Bessel, standard Lotka--Volterra, fractional Lotka--Volterra, and Robertson benchmarks, respectively, while more stable predictions and higher R2 scores are achieved on the damped oscillator benchmark.

DOI
10.21203/rs.3.rs-10778666/v1

Related papers

Hybrid Quantum-Classical Recurrent Neural Networks

Wenduan Xu

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 $\mathbb{C}^{2^n}$, 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.

arXiv:2510.25557•Oct 29, 2025•0 citations

A fully quantum-native recurrent neural network for end-to-end sequential learning on NISQ hardware

Rui Huang, Haibo Yi

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.

Machine Learning Science and Technology•Apr 15, 2026•1 citation

Quantum-Enhanced Recurrent Neural Networks via Variational Quantum Gating for Battery State of Health Prediction

Yin Xu, Qinglin Liu, Li Gao +1 more

Accurate state-of-health (SOH) estimation for lithium-ion batteries remains a challenging problem due to complex electrochemical degradation mechanisms and long-range temporal dependencies. In this work, we propose a quantum-enhanced recurrent framework, termed QLSTM, in which variational quantum circuits are directly embedded into the gating mechanisms of long short-term memory networks. By replacing classical affine transformations with parameterized unitary operations, the proposed model introduces structured nonlinear transformations into the recurrent state-transition process. Extensive experiments on multiple benchmark battery datasets demonstrate that QLSTM consistently outperforms classical sequence models in both predictive accuracy and robustness, achieving significant reductions in mean absolute error (MAE), with improvements on the order of 20% compared with classical LSTM baselines. Ablation studies further confirm that these improvements arise primarily from quantum-enhanced gating rather than input-level transformations. Additional analyses on qubit scaling and noise robustness reveal that model performance is governed by a balance between expressive capacity and trainability. These results provide empirical evidence that embedding quantum computational primitives within recurrent architectures offers a structurally grounded approach to improving sequence modeling capability. The proposed framework establishes a new design paradigm for integrating quantum operators into temporal learning models, with potential applications in complex dynamical system prediction tasks.

quant-pharXiv:2604.20438•Apr 23, 2026•0 citations

Quantum Recurrent Neural Networks for Sequential Learning

Yanan Li, Zhimin Wang, Rongbing Han +6 more

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.

arXiv:2302.03244•Feb 7, 2023•1 citation

A variational approach to quantum gated recurrent units

Andrea Ceschini, Antonello Rosato, Massimo Panella

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.

Journal of Physics Communications•Aug 1, 2024•10 citations

Time-warping invariant quantum recurrent neural networks via quantum-classical adaptive gating

Ivana Nikoloska, Osvaldo Simeone, Leonardo Banchi +1 more

Abstract Adaptive gating plays a key role in temporal data processing via classical recurrent neural networks (RNNs), as it facilitates retention of past information necessary to predict the future, providing a mechanism that preserves invariance to time warping transformations. This paper builds on quantum RNNs (QRNNs), a dynamic model with quantum memory, to introduce a novel class of temporal data processing quantum models that preserve invariance to time-warping transformations of the (classical) input-output sequences. The model, referred to as time warping-invariant QRNN (TWI-QRNN) , augments a QRNN with a quantum–classical adaptive gating mechanism that chooses whether to apply a parameterized unitary transformation at each time step as a function of the past samples of the input sequence via a classical recurrent model. The TWI-QRNN model class is derived from first principles, and its capacity to successfully implement time-warping transformations is experimentally demonstrated on examples with classical or quantum dynamics.

arXiv:2301.08173•Machine Learning Science and Technology•Oct 2, 2023•4 citations
Abstract Quantum recurrent neural networks (QRNNs) have been investigated as a promising paradigm for sequential modeling by integrating parameterized quantum circuits with recurrent architectures. However, existing QRNNs often require additional quantum resources to implement effective gating mechanisms and struggle to capture long-range temporal dependencies. To address these issues, a Conditional Gated Quantum Recurrent Neural Network with Recurrent Temporal Attention (CG-QRNN) is proposed. The Conditional Gating (CG) strategy uses mid-circuit measurement outcomes as control signals to selectively execute subsequent quantum operations within each recurrent update. By coupling intermediate measurement with conditional quantum operations, quantum gating is implemented while the existing qubits are reused, thereby avoiding the introduction of additional qubits for quantum gating. The Recurrent Temporal Attention (RTA) mechanism uses the current hidden state to interact with historical hidden states and dynamically determines their contributions to the current recurrent update. The historical hidden states are then aggregated according to these contributions and incorporated into the current hidden state update. Experiments on five ordinary differential equation benchmarks demonstrate that the CG-QRNN achieves superior overall performance, with average prediction errors reduced by 59.1%, 69.6%, 83.3%, and 97.5% compared with the best-performing baselines on the Bessel, standard Lotka--Volterra, fractional Lotka--Volterra, and Robertson benchmarks, respectively, while more stable predictions and higher R2 scores are achieved on the damped oscillator benchmark.
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 nnn-qubit PQC in an exponentially large Hilbert space C2n\mathbb{C}^{2^n}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.
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.
Accurate state-of-health (SOH) estimation for lithium-ion batteries remains a challenging problem due to complex electrochemical degradation mechanisms and long-range temporal dependencies. In this work, we propose a quantum-enhanced recurrent framework, termed QLSTM, in which variational quantum circuits are directly embedded into the gating mechanisms of long short-term memory networks. By replacing classical affine transformations with parameterized unitary operations, the proposed model introduces structured nonlinear transformations into the recurrent state-transition process. Extensive experiments on multiple benchmark battery datasets demonstrate that QLSTM consistently outperforms classical sequence models in both predictive accuracy and robustness, achieving significant reductions in mean absolute error (MAE), with improvements on the order of 20% compared with classical LSTM baselines. Ablation studies further confirm that these improvements arise primarily from quantum-enhanced gating rather than input-level transformations. Additional analyses on qubit scaling and noise robustness reveal that model performance is governed by a balance between expressive capacity and trainability. These results provide empirical evidence that embedding quantum computational primitives within recurrent architectures offers a structurally grounded approach to improving sequence modeling capability. The proposed framework establishes a new design paradigm for integrating quantum operators into temporal learning models, with potential applications in complex dynamical system prediction tasks.
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.
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.
Abstract Adaptive gating plays a key role in temporal data processing via classical recurrent neural networks (RNNs), as it facilitates retention of past information necessary to predict the future, providing a mechanism that preserves invariance to time warping transformations. This paper builds on quantum RNNs (QRNNs), a dynamic model with quantum memory, to introduce a novel class of temporal data processing quantum models that preserve invariance to time-warping transformations of the (classical) input-output sequences. The model, referred to as time warping-invariant QRNN (TWI-QRNN) , augments a QRNN with a quantum–classical adaptive gating mechanism that chooses whether to apply a parameterized unitary transformation at each time step as a function of the past samples of the input sequence via a classical recurrent model. The TWI-QRNN model class is derived from first principles, and its capacity to successfully implement time-warping transformations is experimentally demonstrated on examples with classical or quantum dynamics.