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arXiv · 2502.12157

From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing

Saud Čindrak·Kathy Lüdge·Lina Jaurigue
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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.

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Saud Čindrak, Kathy Lüdge, Lina Jaurigue. 2025-01-21. From Krylov Complexity to Observability: Capturing Phase Space Dimension with Applications in Quantum Reservoir Computing. https://doi.org/10.1103/m9kq-wrln

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