[2601.22400] Spectral Filtering for Complex Linear Dynamical Systems

Quantum Physics arXiv:2601.22400 (quant-ph) [Submitted on 29 Jan 2026 (v1), last revised 8 May 2026 (this version, v2)] Title:Spectral Filtering for Complex Linear Dynamical Systems Authors:Elad Hazan, Annie Marsden View a PDF of the paper titled Spectral Filtering for Complex Linear Dynamical Systems, by Elad Hazan and 1 other authors View PDF HTML (experimental) Abstract:We study the problem of learning complex-valued linear dynamical systems (CLDS) with sector-bounded spectrum. This class captures oscillatory and long-memory dynamics arising in signal processing, structured state space models, and quantum systems. We introduce a spectral filtering method based on the Slepian basis and show that learnability is governed by an effective dimension independent of the ambient state dimension. As a consequence, we obtain dimension-free regret bounds for sequence prediction in CLDS with spectrum contained in a sector of the unit disk. Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI) Cite as: arXiv:2601.22400 [quant-ph]   (or arXiv:2601.22400v2 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2601.22400 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Elad Hazan [view email] [v1] Thu, 29 Jan 2026 23:11:57 UTC (349 KB) [v2] Fri, 8 May 2026 16:03:52 UTC (6,566 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral Filtering for Complex Linear Dynamical Systems, by Elad Hazan and 1 other authorsView PD...