Diagnosing quantum reservoirs at scale based on expressivity and coverage
Abstract
Quantum reservoirs offer a hardware-friendly route to quantum machine learning, replacing trainable circuits with fixed random dynamics and a classical readout. Because the reservoir is not optimized, performance depends entirely on the choice of reservoir family, yet existing diagnostics demand resources that grow exponentially with system size. We introduce a scalable, hardware-agnostic framework built on two complementary quantities. The first is a task-independent order-statistics (ORS) expressivity score, which compares only the largest output probabilities of a reservoir ensemble against an analytical Haar baseline. It never reconstructs the full output distribution, is cost-independent of Hilbert-space dimension, and admits a closed-form depolarizing noise correction, making it directly usable on hardware. The second is the task-dependent effective rank Reff of the feature matrix, which measures how much input-dependent information reaches the readout. We validate the ORS score against established complexity diagnostics and confirm it remains informative under simulated noise and on IBM quantum hardware. Across synthetic and real quantum extreme learning machine and quantum reservoir computing benchmarks, ORS captures the intrinsic expressivity hierarchy of reservoir families while Reff determines when that expressivity becomes usable predictive information.
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BibTeX
@misc{domingo2026diagnosing,
title = {{Diagnosing quantum reservoirs at scale based on expressivity and coverage}},
author = {Laia Domingo and Oriol Balló-Gimbernat and Fernando Vilariño},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2607.09445},
eprint = {2607.09445},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.09445},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Diagnosing quantum reservoirs at scale based on expressivity and coverage
AU - Laia Domingo
AU - Oriol Balló-Gimbernat
AU - Fernando Vilariño
PY - 2026
DA - 2026/08/28
PB - arXiv
DO - 10.48550/arxiv.2607.09445
UR - https://arxiv.org/abs/2607.09445
AB - Quantum reservoirs offer a hardware-friendly route to quantum machine learning, replacing trainable circuits with fixed random dynamics and a classical readout. Because the reservoir is not optimized, performance depends entirely on the choice of reservoir family, yet existing diagnostics demand resources that grow exponentially with system size. We introduce a scalable, hardware-agnostic framework built on two complementary quantities. The first is a task-independent order-statistics (ORS) expressivity score, which compares only the largest output probabilities of a reservoir ensemble against an analytical Haar baseline. It never reconstructs the full output distribution, is cost-independent of Hilbert-space dimension, and admits a closed-form depolarizing noise correction, making it directly usable on hardware. The second is the task-dependent effective rank R_eff of the feature matrix, which measures how much input-dependent information reaches the readout. We validate the ORS score against established complexity diagnostics and confirm it remains informative under simulated noise and on IBM quantum hardware. Across synthetic and real quantum extreme learning machine and quantum reservoir computing benchmarks, ORS captures the intrinsic expressivity hierarchy of reservoir families while R_eff determines when that expressivity becomes usable predictive information.
ER -