# Extending echo state property for quantum reservoir computing

arXiv: https://arxiv.org/abs/2403.02686 · HTML: https://mlsanity.com/paper/2403.02686/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 20 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Builds on (most cited first, 3 of 3)

- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Temporal Information Processing on Noisy Quantum Computers](https://mlsanity.com/paper/2001.09498/) (2020)
- [Higher-Order Quantum Reservoir Computing](https://mlsanity.com/paper/2006.08999/) (2020)

## Built on by (most cited first, 7 of 7)

- [Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability](https://mlsanity.com/paper/2506.22335/) (2025)
- [Role of scrambling and noise in temporal information processing with quantum systems](https://mlsanity.com/paper/2505.10080/) (2025)
- [Echoes of the Past: A Unified Perspective on Fading memory and Echo States](https://mlsanity.com/paper/2508.19145/) (2025)
- [Lindblad-Inspired Multi-Timescale Reservoir Computing with Separable Rotation and Dissipation](https://mlsanity.com/paper/2608.04028/) (2026)
- [Quantum Reservoir Computing: Recent Advances and Future Directions](https://mlsanity.com/paper/2607.18552/) (2026)
- [Coherent Floquet quantum reservoirs for molecular property prediction](https://mlsanity.com/paper/2609.11071/) (2026)
- [Task-Resolved Fisher Spectroscopy for Quantum Reservoir Computing](https://mlsanity.com/paper/2609.29570/) (2026)

## Abstract (arXiv)

The echo state property (ESP) represents a fundamental concept in the reservoir computing (RC) framework that ensures output-only training of reservoir networks by being agnostic to the initial states and far past inputs. However, the traditional definition of ESP does not describe possible non-stationary systems in which statistical properties evolve. To address this issue, we introduce two new categories of ESP: textitnon-stationary ESP, designed for potentially non-stationary systems, and textitsubspace/subset ESP, designed for systems whose subsystems have ESP. Following the definitions, we numerically demonstrate the correspondence between non-stationary ESP in the quantum reservoir computer (QRC) framework with typical Hamiltonian dynamics and input encoding methods using non-linear autoregressive moving-average (NARMA) tasks. We also confirm the correspondence by computing linear/non-linear memory capacities that quantify input-dependent components within reservoir states. Our study presents a new understanding of the practical design of QRC and other possibly non-stationary RC systems in which non-stationary systems and subsystems are exploited.