# Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics

arXiv: https://arxiv.org/abs/2409.01394 · HTML: https://mlsanity.com/paper/2409.01394/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 48 references that are in the map.
- First posted on arXiv 2 Sep 2024.

## Builds on (most cited first, 10 of 10)

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Robust Optimization and Validation of Echo State Networks for learning chaotic dynamics](https://mlsanity.com/paper/2103.03174/) (2021)
- [On fundamental aspects of quantum extreme learning machines](https://mlsanity.com/paper/2312.15124/) (2023)
- [Reduction of finite sampling noise in quantum neural networks](https://mlsanity.com/paper/2306.01639/) (2023)
- [Dimension of Reservoir Computers](https://mlsanity.com/paper/1912.06472/) (2019)
- [Data-driven prediction and control of extreme events in a chaotic flow](https://mlsanity.com/paper/2204.11682/) (2022)
- [Physics-Informed Echo State Networks for Chaotic Systems Forecasting](https://mlsanity.com/paper/1906.11122/) (2019)
- [Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics](https://mlsanity.com/paper/2308.14239/) (2023)

## Built on by (most cited first, 9 of 9)

- [Feedback-driven recurrent quantum neural network universality](https://mlsanity.com/paper/2506.16332/) (2025)
- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)
- [Multivariate Time Series Forecasting with Gate-Based Quantum Reservoir Computing on NISQ Hardware](https://mlsanity.com/paper/2510.13634/) (2025)
- [Quantum Machine Unlearning: Foundations, Mechanisms, and Taxonomy](https://mlsanity.com/paper/2511.00406/) (2025)
- [Kernel-based optimization of measurement operators for quantum reservoir computers](https://mlsanity.com/paper/2602.14677/) (2026)
- [Theory and interpretability of Quantum Extreme Learning Machines: a Pauli-transfer matrix approach](https://mlsanity.com/paper/2602.18377/) (2026)
- [Quantum Reservoir Computing for Short-Term Power Load Forecasting in Resource-Constrained Energy Systems](https://mlsanity.com/paper/2606.12806/) (2026)
- [Quantum Reservoir Computing: Recent Advances and Future Directions](https://mlsanity.com/paper/2607.18552/) (2026)
- [A Quantum Variational Approach to Prototypical Recurrent Unit](https://mlsanity.com/paper/2609.04354/) (2026)

## Abstract (arXiv)

In the current Noisy Intermediate Scale Quantum (NISQ) era, the presence of noise deteriorates the performance of quantum computing algorithms. Quantum Reservoir Computing (QRC) is a type of Quantum Machine Learning algorithm, which, however, can benefit from different types of tuned noise. In this paper, we analyse the effect that finite-sampling noise has on the chaotic time-series prediction capabilities of QRC and Recurrence-free Quantum Reservoir Computing (RF-QRC). First, we show that, even without a recurrent loop, RF-QRC contains temporal information about previous reservoir states using leaky integrated neurons. This makes RF-QRC different from Quantum Extreme Learning Machines (QELM). Second, we show that finite sampling noise degrades the prediction capabilities of both QRC and RF-QRC while affecting QRC more due to the propagation of noise. Third, we optimize the training of the finite-sampled quantum reservoir computing framework using two methods: (a) Singular Value Decomposition (SVD) applied to the data matrix containing noisy reservoir activation states; and (b) data-filtering techniques to remove the high-frequencies from the noisy reservoir activation states. We show that denoising reservoir activation states improve the signal-to-noise ratios with smaller training loss. Finally, we demonstrate that the training and denoising of the noisy reservoir activation signals in RF-QRC are highly parallelizable on multiple Quantum Processing Units (QPUs) as compared to the QRC architecture with recurrent connections. The analyses are numerically showcased on prototypical chaotic dynamical systems with relevance to turbulence. This work opens opportunities for using quantum reservoir computing with finite samples for time-series forecasting on near-term quantum hardware.