# Rapid training of quantum recurrent neural networks

arXiv: https://arxiv.org/abs/2207.00378 · HTML: https://mlsanity.com/paper/2207.00378/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 83 references that are in the map.
- First posted on arXiv 1 Jul 2022.

## Builds on (most cited first, 26 of 26)

- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Deep Speech 2: End-to-End Speech Recognition in English and Mandarin](https://mlsanity.com/paper/1512.02595/) (2015)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [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)
- [Quantum Machine Learning](https://mlsanity.com/paper/1611.09347/) (2016)
- [Unitary Evolution Recurrent Neural Networks](https://mlsanity.com/paper/1511.06464/) (2015)
- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Gate-Variants of Gated Recurrent Unit (GRU) Neural Networks](https://mlsanity.com/paper/1701.05923/) (2017)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition](https://mlsanity.com/paper/1402.1128/) (2014)
- [Full-Capacity Unitary Recurrent Neural Networks](https://mlsanity.com/paper/1611.00035/) (2016)
- [Recent Advances in Recurrent Neural Networks](https://mlsanity.com/paper/1801.01078/) (2017)
- [Image and Video Compression with Neural Networks: A Review](https://mlsanity.com/paper/1904.03567/) (2019)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Continuous-variable quantum neural networks](https://mlsanity.com/paper/1806.06871/) (2018)
- [Deep Learning for Time-Series Analysis](https://mlsanity.com/paper/1701.01887/) (2017)
- [Minimal Gated Unit for Recurrent Neural Networks](https://mlsanity.com/paper/1603.09420/) (2016)
- [On Circuit-based Hybrid Quantum Neural Networks for Remote Sensing Imagery Classification](https://mlsanity.com/paper/2109.09484/) (2021)
- [Systematic Literature Review: Quantum Machine Learning and its applications](https://mlsanity.com/paper/2201.04093/) (2022)
- [Advances in Quantum Deep Learning: An Overview](https://mlsanity.com/paper/2005.04316/) (2020)
- [Simplified Minimal Gated Unit Variations for Recurrent Neural Networks](https://mlsanity.com/paper/1701.03452/) (2017)

## Built on by (most cited first, 13 of 13)

- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [Approximately Equivariant Quantum Neural Network for p4m Group Symmetries in Images](https://mlsanity.com/paper/2310.02323/) (2023)
- [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)
- [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)
- [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)
- [FRQI Pairs method for image classification using Quantum Recurrent Neural Network](https://mlsanity.com/paper/2512.11499/) (2025)
- [A Quantum-Classical Hybrid Framework for Multivariate Time-Series Forecasting Complexity-Fidelity Trade-offs and Limitations](https://mlsanity.com/paper/2607.16358/) (2026)
- [A Quantum Variational Approach to Prototypical Recurrent Unit](https://mlsanity.com/paper/2609.04354/) (2026)

## Abstract (arXiv)

Time series prediction is essential for human activities in diverse areas. A common approach to this task is to harness Recurrent Neural Networks (RNNs). However, while their predictions are quite accurate, their learning process is complex and, thus, time and energy consuming. Here, we propose to extend the concept of RRNs by including continuous-variable quantum resources in it, and to use a quantum-enhanced RNN to overcome these obstacles. The design of the Continuous-Variable Quantum RNN (CV-QRNN) is rooted in the continuous-variable quantum computing paradigm. By performing extensive numerical simulations, we demonstrate that the quantum network is capable of learning-time dependence of several types of temporal data, and that it converges to the optimal weights in fewer epochs than a classical network. Furthermore, for a small number of trainable parameters, it can achieve lower losses than its classical counterpart. CV-QRNN can be implemented using commercially available quantum-photonic hardware.