# Quantum Recurrent Neural Networks for Sequential Learning

arXiv: https://arxiv.org/abs/2302.03244 · HTML: https://mlsanity.com/paper/2302.03244/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 46 references that are in the map.
- First posted on arXiv 7 Feb 2023.

## Builds on (most cited first, 19 of 19)

- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [Generating Sequences With Recurrent Neural Networks](https://mlsanity.com/paper/1308.0850/) (2013)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [The effect of data encoding on the expressive power of variational quantum machine learning models](https://mlsanity.com/paper/2008.08605/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Absence of Barren Plateaus in Quantum Convolutional Neural Networks](https://mlsanity.com/paper/2011.02966/) (2020)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Noisy intermediate-scale quantum (NISQ) algorithms](https://mlsanity.com/paper/2101.08448/) (2021)
- [A Primer on Neural Network Models for Natural Language Processing](https://mlsanity.com/paper/1510.00726/) (2015)
- [QNLP in Practice: Running Compositional Models of Meaning on a Quantum Computer](https://mlsanity.com/paper/2102.12846/) (2021)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [Quantum Self-Attention Neural Networks for Text Classification](https://mlsanity.com/paper/2205.05625/) (2022)
- [Quantum Neuron: an elementary building block for machine learning on quantum computers](https://mlsanity.com/paper/1711.11240/) (2017)
- [Input Redundancy for Parameterized Quantum Circuits](https://mlsanity.com/paper/1901.11434/) (2019)
- [Sample Complexity of Learning Parametric Quantum Circuits](https://mlsanity.com/paper/2107.09078/) (2021)

## Built on by (most cited first, 25 of 25)

- [A Survey on Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead](https://mlsanity.com/paper/2310.10315/) (2023)
- [Quantum Mixed-State Self-Attention Network](https://mlsanity.com/paper/2403.02871/) (2024)
- [Feedback-driven recurrent quantum neural network universality](https://mlsanity.com/paper/2506.16332/) (2025)
- [Density Matrix Emulation of Quantum Recurrent Neural Networks for Multivariate Time Series Prediction](https://mlsanity.com/paper/2310.20671/) (2023)
- [Learning to Learn with Quantum Optimization via Quantum Neural Networks](https://mlsanity.com/paper/2505.00561/) (2025)
- [MerLin: A Discovery Engine for Photonic and Hybrid Quantum Machine Learning](https://mlsanity.com/paper/2602.11092/) (2026)
- [Optimizing Quantum Convolutional Neural Network Architectures for Arbitrary Data Dimension](https://mlsanity.com/paper/2403.19099/) (2024)
- [Quantum vs. Classical Machine Learning: A Benchmark Study for Financial Prediction](https://mlsanity.com/paper/2601.03802/) (2026)
- [Recursive QLSTM with Dynamic Variational Quantum Circuit Adaptation](https://mlsanity.com/paper/2606.24932/) (2026)
- [Self-Modulating Quantum Fast-Weight Programmers for Efficient Adaptive Sequential Learning](https://mlsanity.com/paper/2606.24933/) (2026)
- [A Survey of Classical And Quantum Sequence Models](https://mlsanity.com/paper/2312.10242/) (2023)
- [Exploring Quantum Machine Learning for Weather Forecasting](https://mlsanity.com/paper/2509.01422/) (2025)
- [Hybrid Quantum-Classical Recurrent Neural Networks](https://mlsanity.com/paper/2510.25557/) (2025)
- [Quantum Circuit-Based Learning Models: Bridging Quantum Computing and Machine Learning](https://mlsanity.com/paper/2602.00048/) (2026)
- [Multi-Scale Feature Fusion Quantum Depthwise Convolutional Neural Networks for Text Classification](https://mlsanity.com/paper/2405.13515/) (2024)
- [EQNN: Enhanced Quantum Neural Network](https://mlsanity.com/paper/2411.17726/) (2024)
- [An Efficient Quantum Classifier Based on Hamiltonian Representations](https://mlsanity.com/paper/2504.10542/) (2025)
- [Quantum Observers: A NISQ Hardware Demonstration of Chaotic State Prediction Using Quantum Echo-state Networks](https://mlsanity.com/paper/2505.06799/) (2025)
- [Hybrid Quantum-Classical Selective State Space Artificial Intelligence](https://mlsanity.com/paper/2511.08349/) (2025)
- [Hybrid Quantum Temporal Convolutional Networks](https://mlsanity.com/paper/2602.23578/) (2026)
- [QLAM: A Quantum Long-Attention Memory Approach to Long-Sequence Token Modeling](https://mlsanity.com/paper/2605.13833/) (2026)
- [Complementary Matrix-Gated QKAN Fast-Weight Programmers for Quantum Dynamics Forecasting](https://mlsanity.com/paper/2607.27945/) (2026)
- [A Quantum Variational Approach to Prototypical Recurrent Unit](https://mlsanity.com/paper/2609.04354/) (2026)
- [QiT: Quantum-Inspired Transformer for Visual Recognition Task](https://mlsanity.com/paper/2609.17789/) (2026)
- [Trainable Quantum-Native Language Models: Dissipative Memory, Capacity Limits, and Hardware Validation](https://mlsanity.com/paper/2610.12806/) (2026)

## Abstract (arXiv)

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.