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QI: Fachverband Quanteninformation

QI 2: Quantum Machine Learning I

QI 2.5: Vortrag

Montag, 10. März 2025, 12:00–12:15, HS VIII

Quantum reservoir computing maps data onto the Krylov space — •Saud Cindrak, Lina Jaurigue, and Kathy Lüdge — Technische Universität Ilmenau, Ilmenau, Deutschland

The field of Krylov complexity has deepened our understanding of quantum systems, from field theories to chaos, and shed light on quantum evolution. However, classical computation of these complexities becomes infeasible for larger systems. We address this by defining a measurable basis to construct the Krylov space and introducing Krylov expressivity to capture the phase space dimension [1]. Additionally, we define Krylov observability, which quantifies how much of the phase space is observed. This work examines fidelity, spread complexity, Krylov expressivity, and Krylov observability as expressivity measures in quantum reservoir computing. In this approach, data is encoded into the system’s state, evolved through the quantum system, and measured observables construct a readout vector, which is trained to predict chaotic attractors and compute the information processing capacity. Our findings show that fidelity and spread complexity provide limited insights, while Krylov expressivity effectively captures task performance [2]. Notably, Krylov observability and the information processing capacity exhibit almost identical behavior, demonstrating that a quantum reservoir maps data onto the Krylov space.
[1]  S. Čindrak, L. Jaurigue, K.Lüdge, J. High Energ. Phys 2024, 83
[2]  S. Čindrak, L. Jaurigue, K.Lüdge, arxiv.org/abs/2409.12079

Keywords: Krylov complexity; Quantum reservoir computing; Quantum machine learning; Quantum expressivity