# Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability

arXiv: https://arxiv.org/abs/2506.22335 · HTML: https://mlsanity.com/paper/2506.22335/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 88 references that are in the map.
- First posted on arXiv 27 Jun 2025.

## Builds on (most cited first, 19 of 19)

- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Backpropagation Algorithms and Reservoir Computing in Recurrent Neural Networks for the Forecasting of Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/1910.05266/) (2019)
- [Barren Plateaus in Variational Quantum Computing](https://mlsanity.com/paper/2405.00781/) (2024)
- [A Systematic Exploration of Reservoir Computing for Forecasting Complex Spatiotemporal Dynamics](https://mlsanity.com/paper/2201.08910/) (2022)
- [On fundamental aspects of quantum extreme learning machines](https://mlsanity.com/paper/2312.15124/) (2023)
- [Learn to Synchronize, Synchronize to Learn](https://mlsanity.com/paper/2010.02860/) (2020)
- [Attractor reconstruction with reservoir computers: The effect of the reservoir's conditional Lyapunov exponents on faithful attractor reconstruction](https://mlsanity.com/paper/2401.00885/) (2023)
- [Optimal training of finitely-sampled quantum reservoir computers for forecasting of chaotic dynamics](https://mlsanity.com/paper/2409.01394/) (2024)
- [Reconstruction, forecasting, and stability of chaotic dynamics from partial data](https://mlsanity.com/paper/2305.15111/) (2023)
- [Extending echo state property for quantum reservoir computing](https://mlsanity.com/paper/2403.02686/) (2024)
- [Stability analysis of chaotic systems in latent spaces](https://mlsanity.com/paper/2410.00480/) (2024)
- [Data-driven prediction and control of extreme events in a chaotic flow](https://mlsanity.com/paper/2204.11682/) (2022)
- [Quantum Next Generation Reservoir Computing: An Efficient Quantum Algorithm for Forecasting Quantum Dynamics](https://mlsanity.com/paper/2308.14239/) (2023)
- [Gradient-free optimization of chaotic acoustics with reservoir computing](https://mlsanity.com/paper/2106.09780/) (2021)
- [Learning ergodic averages in chaotic systems](https://mlsanity.com/paper/2001.04027/) (2020)
- [Coherence influx is indispensable for quantum reservoir computing](https://mlsanity.com/paper/2409.12693/) (2024)
- [Statistical prediction of extreme events from small datasets](https://mlsanity.com/paper/2201.08294/) (2022)

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

- [Sustained Performance and Energy Accounting for Nonlinear Forecasting Across Classical and Simulated Quantum Models](https://mlsanity.com/paper/2510.25183/) (2025)
- [Sequential Reservoir Computing for Efficient High-Dimensional Spatiotemporal Forecasting](https://mlsanity.com/paper/2601.00172/) (2026)
- [Controllable Quantum Memory Capacity in Quantum Reservoir Networks with Tunable partial-SWAPs](https://mlsanity.com/paper/2605.12713/) (2026)
- [Quantum Reservoir Computing: Recent Advances and Future Directions](https://mlsanity.com/paper/2607.18552/) (2026)
- [Quantum Reservoir Computing with Physics-Informed Correction for Reduced-Order PDE Forecasting](https://mlsanity.com/paper/2608.23119/) (2026)

## Abstract (arXiv)

We show that recurrent quantum reservoir computers (QRCs) and their recurrence-free architectures (RF-QRCs) are robust tools for learning and forecasting chaotic dynamics from time-series data. First, we formulate and interpret quantum reservoir computers as coupled dynamical systems, where the reservoir acts as a response system driven by training data; in other words, quantum reservoir computers are generalized-synchronization (GS) systems. Second, we show that quantum reservoir computers can learn chaotic dynamics and their invariant properties, such as Lyapunov spectra, attractor dimensions, and geometric properties such as the covariant Lyapunov vectors. This analysis is enabled by deriving the Jacobian of the quantum reservoir update. Third, by leveraging tools from generalized synchronization, we provide a method for designing robust quantum reservoir computers. We propose the criterion GS=ESP: GS implies the echo state property (ESP), and vice versa. We analytically show that RF-QRCs, by design, fulfill GS=ESP. Finally, we analyze the effect of simulated noise. We find that dissipation from noise enhances the robustness of quantum reservoir computers. Numerical verifications on systems of different dimensions support our conclusions. This work opens opportunities for designing robust quantum machines for chaotic time series forecasting on near-term quantum hardware.