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  • Letter
  • Open Access

From Krylov complexity to observability: Capturing phase space dimension with applications in quantum reservoir computing

Saud Čindrak*, Kathy Lüdge, and Lina Jaurigue

  • *Contact author: saud.cindrak@tu-ilmenau.de
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Phys. Rev. Research 7, L042039 – Published 20 November, 2025

DOI: https://doi.org/10.1103/m9kq-wrln

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 are mapped onto the Krylov space.

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See Also

Engineering quantum reservoirs through Krylov complexity, expressivity, and observability

Saud Čindrak, Lina Jaurigue, and Kathy Lüdge
Phys. Rev. Research 7, 043190 (2025)

Article Text

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Phys. Rev. Research 7, L042039– Published 20 November, 2025
  • Received 13 February 2025
  • Accepted 22 August 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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