# Quantum Observers: A NISQ Hardware Demonstration of Chaotic State Prediction Using Quantum Echo-state Networks

arXiv: https://arxiv.org/abs/2505.06799 · HTML: https://mlsanity.com/paper/2505.06799/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 47 references that are in the map.
- First posted on arXiv 11 May 2025.

## Builds on (most cited first, 11 of 11)

- [A rigorous and robust quantum speed-up in supervised machine learning](https://mlsanity.com/paper/2010.02174/) (2020)
- [Challenges and Opportunities in Quantum Machine Learning](https://mlsanity.com/paper/2303.09491/) (2023)
- [Supervised quantum machine learning models are kernel methods](https://mlsanity.com/paper/2101.11020/) (2021)
- [Quantum advantage in learning from experiments](https://mlsanity.com/paper/2112.00778/) (2021)
- [Quantum Graph Neural Networks](https://mlsanity.com/paper/1909.12264/) (2019)
- [On the Quantum versus Classical Learnability of Discrete Distributions](https://mlsanity.com/paper/2007.14451/) (2020)
- [Quantum Recurrent Neural Networks for Sequential Learning](https://mlsanity.com/paper/2302.03244/) (2023)
- [Temporal Information Processing on Noisy Quantum Computers](https://mlsanity.com/paper/2001.09498/) (2020)
- [Quantum Computing: A Taxonomy, Systematic Review and Future Directions](https://mlsanity.com/paper/2010.15559/) (2020)
- [Learning with SASQuaTCh: a Novel Variational Quantum Transformer Architecture with Kernel-Based Self-Attention](https://mlsanity.com/paper/2403.14753/) (2024)
- [Interpretable Design of Reservoir Computing Networks using Realization Theory](https://mlsanity.com/paper/2112.06891/) (2021)

## Abstract (arXiv)

Recent advances in artificial intelligence have highlighted the remarkable capabilities of neural network (NN)-powered systems on classical computers. However, these systems face significant computational challenges that limit scalability and efficiency. Quantum computers hold the potential to overcome these limitations and increase processing power beyond classical systems. Despite this, integrating quantum computing with NNs remains largely unrealized due to challenges posed by noise, decoherence, and high error rates in current quantum hardware. Here, we propose a novel quantum echo-state network (QESN) design and implementation algorithm that can operate within the presence of noise on current IBM hardware. We apply classical control-theoretic response analysis to characterize the QESN, emphasizing its rich nonlinear dynamics and memory, as well as its ability to be fine-tuned with sparsity and re-uploading blocks. We validate our approach through a comprehensive demonstration of QESNs functioning as quantum observers, applied in both high-fidelity simulations and hardware experiments utilizing data from a prototypical chaotic Lorenz system. Our results show that the QESN can predict long time-series with persistent memory, running over 100 times longer than the median T1 and T2 of the IBM Marrakesh QPU, achieving state-of-the-art time-series performance on superconducting hardware.