When Can Quantum Extreme Learning Machines Replace Quantum Reservoirs?
Abstract
Quantum reservoir computers (QRCs) retain information from earlier inputs, whereas reset-window quantum extreme learning machines (QELMs) start afresh and receive only a recent input window. We establish when this window can replace the reservoir's memory. Under our stated assumptions and with exact expectation values, sufficiently expressive QELMs can reproduce reservoir outputs arbitrarily accurately as their windows grow precisely when the influence of the omitted past becomes uniformly negligible. However, longer windows do not always solve the problem. We construct a simple two-qubit reservoir that performs temporal recall exactly, while every fixed-window predictor faces the same positive worst-case error over unbounded delays, regardless of model capacity. Analytical benchmarks and simulations distinguish missing history from limited features and finite measurements. The central conclusion is simple: better representations can improve how available information is used, but cannot recover a past the model never receives.
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BibTeX
@misc{baumann2026when,
title = {{When Can Quantum Extreme Learning Machines Replace Quantum Reservoirs?}},
author = {Markus Baumann and Gerhard Stenzel and Jonas Stein and Claudia Linnhoff-Popien},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31027},
eprint = {2609.31027},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31027},
}
RIS
TY - UNPB
TI - When Can Quantum Extreme Learning Machines Replace Quantum Reservoirs?
AU - Markus Baumann
AU - Gerhard Stenzel
AU - Jonas Stein
AU - Claudia Linnhoff-Popien
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.31027
UR - https://arxiv.org/abs/2609.31027
AB - Quantum reservoir computers (QRCs) retain information from earlier inputs, whereas reset-window quantum extreme learning machines (QELMs) start afresh and receive only a recent input window. We establish when this window can replace the reservoir's memory. Under our stated assumptions and with exact expectation values, sufficiently expressive QELMs can reproduce reservoir outputs arbitrarily accurately as their windows grow precisely when the influence of the omitted past becomes uniformly negligible. However, longer windows do not always solve the problem. We construct a simple two-qubit reservoir that performs temporal recall exactly, while every fixed-window predictor faces the same positive worst-case error over unbounded delays, regardless of model capacity. Analytical benchmarks and simulations distinguish missing history from limited features and finite measurements. The central conclusion is simple: better representations can improve how available information is used, but cannot recover a past the model never receives.
ER -