# Quantum Reservoir Computing and Risk Bounds

arXiv: https://arxiv.org/abs/2501.08640 · HTML: https://mlsanity.com/paper/2501.08640/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 41 references that are in the map.
- First posted on arXiv 15 Jan 2025.

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

- [Barren plateaus in quantum neural network training landscapes](https://mlsanity.com/paper/1803.11173/) (2018)
- [Generalization in quantum machine learning from few training data](https://mlsanity.com/paper/2111.05292/) (2021)
- [Echo state networks are universal](https://mlsanity.com/paper/1806.00797/) (2018)
- [Physical reservoir computing -- An introductory perspective](https://mlsanity.com/paper/2005.00992/) (2020)
- [Universal discrete-time reservoir computers with stochastic inputs and linear readouts using non-homogeneous state-affine systems](https://mlsanity.com/paper/1712.00754/) (2017)
- [Model scale versus domain knowledge in statistical forecasting of chaotic systems](https://mlsanity.com/paper/2303.08011/) (2023)
- [On the statistical complexity of quantum circuits](https://mlsanity.com/paper/2101.06154/) (2021)
- [Temporal Information Processing on Noisy Quantum Computers](https://mlsanity.com/paper/2001.09498/) (2020)
- [Risk bounds for reservoir computing](https://mlsanity.com/paper/1910.13886/) (2019)
- [Universal Approximation Theorem and error bounds for quantum neural networks and quantum reservoirs](https://mlsanity.com/paper/2307.12904/) (2023)
- [Learning Nonlinear Input-Output Maps with Dissipative Quantum Systems](https://mlsanity.com/paper/1901.01653/) (2019)

## Built on by (most cited first, 2 of 2)

- [Feedback-driven recurrent quantum neural network universality](https://mlsanity.com/paper/2506.16332/) (2025)
- [QuaRK: A Quantum Reservoir Kernel for Time Series Learning](https://mlsanity.com/paper/2602.13531/) (2026)

## Abstract (arXiv)

We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the generalisation bounds scale with growing numbers of qubits. Applying our results to classes with polynomial readout functions, we find that the risk bounds converge in the number of training samples. The explicit dependence on the quantum reservoir and readout parameters in our bounds can be used to control the generalisation error to a certain extent. It should be noted that the bounds scale exponentially with the number of qubits n. The upper bounds on the Rademacher complexity can be applied to other reservoir classes that fulfill a few hypotheses on the quantum dynamics and the readout function.