# Reservoir Computing via Quantum Recurrent Neural Networks

arXiv: https://arxiv.org/abs/2211.02612 · HTML: https://mlsanity.com/paper/2211.02612/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 50 of its 119 references that are in the map.
- First posted on arXiv 4 Nov 2022.

## Builds on (most cited first, 30 of 50)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Mastering Atari, Go, Chess and Shogi by Planning with a Learned Model](https://mlsanity.com/paper/1911.08265/) (2019)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Speech Recognition with Deep Recurrent Neural Networks](https://mlsanity.com/paper/1303.5778/) (2013)
- [Supervised learning with quantum enhanced feature spaces](https://mlsanity.com/paper/1804.11326/) (2018)
- [The power of quantum neural networks](https://mlsanity.com/paper/2011.00027/) (2020)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Agent57: Outperforming the Atari Human Benchmark](https://mlsanity.com/paper/2003.13350/) (2020)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Variational Quantum Circuits for Deep Reinforcement Learning](https://mlsanity.com/paper/1907.00397/) (2019)
- [Quantum generative adversarial networks](https://mlsanity.com/paper/1804.08641/) (2018)
- [Quantum Long Short-Term Memory](https://mlsanity.com/paper/2009.01783/) (2020)
- [Transfer learning in hybrid classical-quantum neural networks](https://mlsanity.com/paper/1912.08278/) (2019)
- [Long Short-Term Memory Based Recurrent Neural Network Architectures for Large Vocabulary Speech Recognition](https://mlsanity.com/paper/1402.1128/) (2014)
- [Robust data encodings for quantum classifiers](https://mlsanity.com/paper/2003.01695/) (2020)
- [Voice2Series: Reprogramming Acoustic Models for Time Series Classification](https://mlsanity.com/paper/2106.09296/) (2021)
- [Recent Advances in Recurrent Neural Networks](https://mlsanity.com/paper/1801.01078/) (2017)
- [Federated Quantum Machine Learning](https://mlsanity.com/paper/2103.12010/) (2021)
- [Recurrent Quantum Neural Networks](https://mlsanity.com/paper/2006.14619/) (2020)
- [Reinforcement Learning with Quantum Variational Circuits](https://mlsanity.com/paper/2008.07524/) (2020)
- [Quantum Convolutional Neural Networks for High Energy Physics Data Analysis](https://mlsanity.com/paper/2012.12177/) (2020)
- [The Dawn of Quantum Natural Language Processing](https://mlsanity.com/paper/2110.06510/) (2021)
- [Decentralizing Feature Extraction with Quantum Convolutional Neural Network for Automatic Speech Recognition](https://mlsanity.com/paper/2010.13309/) (2020)
- [Quantum Federated Learning with Quantum Data](https://mlsanity.com/paper/2106.00005/) (2021)

## Built on by (most cited first, 14 of 14)

- [Learning to Program Variational Quantum Circuits with Fast Weights](https://mlsanity.com/paper/2402.17760/) (2024)
- [Asynchronous training of quantum reinforcement learning](https://mlsanity.com/paper/2301.05096/) (2023)
- [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)
- [An Introduction to Quantum Reinforcement Learning (QRL)](https://mlsanity.com/paper/2409.05846/) (2024)
- [Differentiable Quantum Architecture Search in Quantum-Enhanced Neural Network Parameter Generation](https://mlsanity.com/paper/2505.09653/) (2025)
- [Time-Warping Invariant Quantum Recurrent Neural Networks via Quantum-Classical Adaptive Gating](https://mlsanity.com/paper/2301.08173/) (2023)
- [Quantum Long Short-term Memory with Differentiable Architecture Search](https://mlsanity.com/paper/2508.14955/) (2025)
- [Gated QKAN-FWP: Scalable Quantum-inspired Sequence Learning](https://mlsanity.com/paper/2605.06734/) (2026)
- [Quantum deep Q learning with distributed prioritized experience replay](https://mlsanity.com/paper/2304.09648/) (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)
- [Quantum Recurrent Neural Networks with Encoder-Decoder for Time-Dependent Partial Differential Equations](https://mlsanity.com/paper/2502.13370/) (2025)
- [Quantum-Assisted Machine Learning Models for Enhanced Weather Prediction](https://mlsanity.com/paper/2503.23408/) (2025)

## Abstract (arXiv)

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.