# Recurrent Quantum Neural Networks

arXiv: https://arxiv.org/abs/2006.14619 · HTML: https://mlsanity.com/paper/2006.14619/

## Key facts

- Cited by 80 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2020.

## Built on by (most cited first, 30 of 80)

- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Better than classical? The subtle art of benchmarking quantum machine learning models](https://mlsanity.com/paper/2403.07059/) (2024)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [Quantum Architecture Search via Deep Reinforcement Learning](https://mlsanity.com/paper/2104.07715/) (2021)
- [Variational Quantum Reinforcement Learning via Evolutionary Optimization](https://mlsanity.com/paper/2109.00540/) (2021)
- [Learning to Decode the Surface Code with a Recurrent, Transformer-Based Neural Network](https://mlsanity.com/paper/2310.05900/) (2023)
- [Recent Advances for Quantum Neural Networks in Generative Learning](https://mlsanity.com/paper/2206.03066/) (2022)
- [Advances and Open Challenges in Federated Foundation Models](https://mlsanity.com/paper/2404.15381/) (2024)
- [Subtleties in the trainability of quantum machine learning models](https://mlsanity.com/paper/2110.14753/) (2021)
- [Systematic Literature Review: Quantum Machine Learning and its applications](https://mlsanity.com/paper/2201.04093/) (2022)
- [Quantum machine learning with differential privacy](https://mlsanity.com/paper/2103.06232/) (2021)
- [A Survey on Quantum Machine Learning: Current Trends, Challenges, Opportunities, and the Road Ahead](https://mlsanity.com/paper/2310.10315/) (2023)
- [QSAN: A Near-term Achievable Quantum Self-Attention Network](https://mlsanity.com/paper/2207.07563/) (2022)
- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [Quantum deep recurrent reinforcement learning](https://mlsanity.com/paper/2210.14876/) (2022)
- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Quantum Architecture Search via Continual Reinforcement Learning](https://mlsanity.com/paper/2112.05779/) (2021)
- [Let Quantum Neural Networks Choose Their Own Frequencies](https://mlsanity.com/paper/2309.03279/) (2023)
- [Hybrid Quantum-Classical Graph Convolutional Network](https://mlsanity.com/paper/2101.06189/) (2021)
- [Quantum Neural Networks: Concepts, Applications, and Challenges](https://mlsanity.com/paper/2108.01468/) (2021)
- [Analytic theory for the dynamics of wide quantum neural networks](https://mlsanity.com/paper/2203.16711/) (2022)
- [Quantum Self-Supervised Learning](https://mlsanity.com/paper/2103.14653/) (2021)
- [The dilemma of quantum neural networks](https://mlsanity.com/paper/2106.04975/) (2021)
- [Learning shallow quantum circuits](https://mlsanity.com/paper/2401.10095/) (2024)
- [Quantum Long Short-Term Memory (QLSTM) vs Classical LSTM in Time Series Forecasting: A Comparative Study in Solar Power Forecasting](https://mlsanity.com/paper/2310.17032/) (2023)
- [Federated Quantum Long Short-term Memory (FedQLSTM)](https://mlsanity.com/paper/2312.14309/) (2023)
- [Reservoir Computing via Quantum Recurrent Neural Networks](https://mlsanity.com/paper/2211.02612/) (2022)
- [Efficient quantum recurrent reinforcement learning via quantum reservoir computing](https://mlsanity.com/paper/2309.07339/) (2023)
- [Differentiable Quantum Architecture Search in Asynchronous Quantum Reinforcement Learning](https://mlsanity.com/paper/2407.18202/) (2024)

## Abstract (arXiv)

Recurrent neural networks are the foundation of many sequence-to-sequence models in machine learning, such as machine translation and speech synthesis. In contrast, applied quantum computing is in its infancy. Nevertheless there already exist quantum machine learning models such as variational quantum eigensolvers which have been used successfully e.g. in the context of energy minimization tasks. In this work we construct a quantum recurrent neural network (QRNN) with demonstrable performance on non-trivial tasks such as sequence learning and integer digit classification. The QRNN cell is built from parametrized quantum neurons, which, in conjunction with amplitude amplification, create a nonlinear activation of polynomials of its inputs and cell state, and allow the extraction of a probability distribution over predicted classes at each step. To study the model's performance, we provide an implementation in pytorch, which allows the relatively efficient optimization of parametrized quantum circuits with thousands of parameters. We establish a QRNN training setup by benchmarking optimization hyperparameters, and analyse suitable network topologies for simple memorisation and sequence prediction tasks from Elman's seminal paper (1990) on temporal structure learning. We then proceed to evaluate the QRNN on MNIST classification, both by feeding the QRNN each image pixel-by-pixel; and by utilising modern data augmentation as preprocessing step. Finally, we analyse to what extent the unitary nature of the network counteracts the vanishing gradient problem that plagues many existing quantum classifiers and classical RNNs.