From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing
Quantum Physics
2026-03-10 v2
Abstract
We demonstrate that time-evolved operators can construct a Krylov space to compute Operator complexity and introduce Krylov observability as a measure of effective phase space dimension in quantum systems. We test Krylov observability in the framework of quantum reservoir computing and show that it closely mirrors information processing capacity, a data-driven expressivity metric, while achieving computation times that are orders of magnitude faster. Our results validate Operator complexity and give the interpretation that data in a quantum reservoir is mapped onto the Krylov space.
Cite
@article{arxiv.2502.12157,
title = {From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing},
author = {Saud Čindrak and Kathy Lüdge and Lina Jaurigue},
journal= {arXiv preprint arXiv:2502.12157},
year = {2026}
}