# Higher-Order Quantum Reservoir Computing

arXiv: https://arxiv.org/abs/2006.08999 · HTML: https://mlsanity.com/paper/2006.08999/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2020.

## Built on by (most cited first, 10 of 10)

- [Learning Temporal Quantum Tomography](https://mlsanity.com/paper/2103.13973/) (2021)
- [Infinite-dimensional reservoir computing](https://mlsanity.com/paper/2304.00490/) (2023)
- [Extending echo state property for quantum reservoir computing](https://mlsanity.com/paper/2403.02686/) (2024)
- [Multivariate Time Series Forecasting with Gate-Based Quantum Reservoir Computing on NISQ Hardware](https://mlsanity.com/paper/2510.13634/) (2025)
- [Iterative Quantum Feature Maps](https://mlsanity.com/paper/2506.19461/) (2025)
- [Quantum Noise-Induced Reservoir Computing](https://mlsanity.com/paper/2207.07924/) (2022)
- [Quantum-Classical Hybrid Information Processing via a Single Quantum System](https://mlsanity.com/paper/2209.00497/) (2022)
- [Higher order quantum reservoir computing for non-intrusive reduced-order models](https://mlsanity.com/paper/2407.21602/) (2024)
- [Vestibular reservoir computing](https://mlsanity.com/paper/2604.09943/) (2026)
- [Quantum Reservoir Computing: Recent Advances and Future Directions](https://mlsanity.com/paper/2607.18552/) (2026)

## Abstract (arXiv)

Quantum reservoir computing (QRC) is an emerging paradigm for harnessing the natural dynamics of quantum systems as computational resources that can be used for temporal machine learning tasks. In the current setup, QRC is difficult to deal with high-dimensional data and has a major drawback of scalability in physical implementations. We propose higher-order QRC, a hybrid quantum-classical framework consisting of multiple but small quantum systems that are mutually communicated via classical connections like linear feedback. By utilizing the advantages of both classical and quantum techniques, our framework enables an efficient implementation to boost the scalability and performance of QRC. Furthermore, higher-order settings allow us to implement a FORCE learning or an innate training scheme, which provides flexibility and high operability to harness high-dimensional quantum dynamics and significantly extends the application domain of QRC. We demonstrate the effectiveness of our framework in emulating large-scale nonlinear dynamical systems, including complex spatiotemporal chaos, which outperforms many of the existing machine learning techniques in certain situations.