Dresden 2026 – wissenschaftliches Programm

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QI: Fachverband Quanteninformation

QI 10: Quantum Information: Concepts and Methods I

QI 10.4: Vortrag

Mittwoch, 11. März 2026, 10:15–10:30, BEY/0137

Understanding Quantum Reservoir Computing through the lens of Krylov Complexity — •Saud Cindrak, Lina Jaurigue, and Kathy Lüdge — Technische Universität Ilmenau, Ilmenau, Deutschland

Recent years have seen growing interest in using information-theoretic and dynamical measures to characterize quantum systems. Krylov complexity, in particular, quantifies how an operator or state spreads within a Krylov basis and distinguishes integrable from chaotic dynamics.

Here we show that time-evolved states and operators generate the same Krylov space, leading to a natural formulation of time-dependent Krylov spaces. Instead of relying on Krylov complexity, we introduce an effective phase-space dimension on the Krylov space that does not inherently assign larger complexity to states deeper in the Krylov chain. We term this measure Krylov observability (for operators) and Krylov expressivity (for states).

We then compare Krylov observability with the data generalizability of a quantum reservoir computer, quantified by its information processing capacity (IPC), and find that the two exhibit almost identical behavior. Lastly, we introduce a quantum Zeno time for operators and use it to further clarify the behavior of Krylov observability up to the Heisenberg time obtained from level statistics.

[1] S. Čindrak, L. Jaurigue, K.Lüdge, Phys. Rev. Res. 7, L042039

[2] S. Čindrak, L. Jaurigue, K.Lüdge, Phys. Rev. Res. 7, 043190

[3] S. Čindrak, L. Jaurigue, K.Lüdge, J. High Energ. Phys 2024, 83

Keywords: Krylov Complexity; Quantum Reservoir Computing; Quantum Machine Learning