# Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics

arXiv: https://arxiv.org/abs/2308.14239 · HTML: https://mlsanity.com/paper/2308.14239/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 63 references that are in the map.
- First posted on arXiv 28 Aug 2023.

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

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Next Generation Reservoir Computing](https://mlsanity.com/paper/2106.07688/) (2021)
- [A quantum-inspired classical algorithm for recommendation systems](https://mlsanity.com/paper/1807.04271/) (2018)
- [Out-of-distribution generalization for learning quantum dynamics](https://mlsanity.com/paper/2204.10268/) (2022)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Echo State Networks trained by Tikhonov least squares are L2(μ) approximators of ergodic dynamical systems](https://mlsanity.com/paper/2005.06967/) (2020)
- [Learning Spatiotemporal Chaos Using Next-Generation Reservoir Computing](https://mlsanity.com/paper/2203.13294/) (2022)
- [The power and limitations of learning quantum dynamics incoherently](https://mlsanity.com/paper/2303.12834/) (2023)
- [Quantum Regularized Least Squares](https://mlsanity.com/paper/2206.13143/) (2022)

## Built on by (most cited first, 5 of 5)

- [On fundamental aspects of quantum extreme learning machines](https://mlsanity.com/paper/2312.15124/) (2023)
- [Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics](https://mlsanity.com/paper/2409.01394/) (2024)
- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)
- [Dissipation alters modes of information encoding in small quantum reservoirs near criticality](https://mlsanity.com/paper/2412.18290/) (2024)
- [Role of scrambling and noise in temporal information processing with quantum systems](https://mlsanity.com/paper/2505.10080/) (2025)

## Abstract (arXiv)

Next Generation Reservoir Computing (NG-RC) is a modern class of model-free machine learning that enables an accurate forecasting of time series data generated by dynamical systems. We demonstrate that NG-RC can accurately predict full many-body quantum dynamics in both integrable and chaotic systems. This is in contrast to the conventional application of reservoir computing that concentrates on the prediction of the dynamics of observables. In addition, we apply a technique which we refer to as skipping ahead to predict far future states accurately without the need to extract information about the intermediate states. However, adopting a classical NG-RC for many-body quantum dynamics prediction is computationally prohibitive due to the large Hilbert space of sample input data. In this work, we propose an end-to-end quantum algorithm for many-body quantum dynamics forecasting with a quantum computational speedup via the block-encoding technique. This proposal presents an efficient model-free quantum scheme to forecast quantum dynamics coherently, bypassing inductive biases incurred in a model-based approach.