Spectral Filtering for Learning Quantum Dynamics

Quantum Physics arXiv:2601.22400 (quant-ph) [Submitted on 29 Jan 2026] Title:Spectral Filtering for Learning Quantum Dynamics Authors:Elad Hazan, Annie Marsden View a PDF of the paper titled Spectral Filtering for Learning Quantum Dynamics, by Elad Hazan and 1 other authors View PDF HTML (experimental) Abstract:Learning high-dimensional quantum systems is a fundamental challenge that notoriously suffers from the curse of dimensionality. We formulate the task of predicting quantum evolution in the linear response regime as a specific instance of learning a Complex-Valued Linear Dynamical System (CLDS) with sector-bounded eigenvalues -- a setting that also encompasses modern Structured State Space Models (SSMs). While traditional system identification attempts to reconstruct full system matrices (incurring exponential cost in the Hilbert dimension), we propose Quantum Spectral Filtering, a method that shifts the goal to improper dynamic learning. Leveraging the optimal concentration properties of the Slepian basis, we prove that the learnability of such systems is governed strictly by an effective quantum dimension $k^*$, determined by the spectral bandwidth and memory horizon. This result establishes that complex-valued LDSs can be learned with sample and computational complexity independent of the ambient state dimension, provided their spectrum is bounded. Subjects: Quantum Physics (quant-ph); Artificial Intelligence (cs.AI) Cite as: arXiv:2601.22400 [quant-ph] (or arXiv:2601.22400v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.22400 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Elad Hazan [view email] [v1] Thu, 29 Jan 2026 23:11:57 UTC (349 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral Filtering for Learning Quantum Dynamics, by Elad Hazan and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cs cs.AI References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)