Krylov's State Complexity and Information Geometry in Qubit Dynamics

Quantum Physics arXiv:2601.18941 (quant-ph) [Submitted on 26 Jan 2026] Title:Krylov's State Complexity and Information Geometry in Qubit Dynamics Authors:Carlo Cafaro, Emma Clements, Vishnu Vardhan Anuboyina View a PDF of the paper titled Krylov's State Complexity and Information Geometry in Qubit Dynamics, by Carlo Cafaro and 2 other authors View PDF HTML (experimental) Abstract:We compare Krylov's state complexity with an information-geometric (IG) measure of complexity for the quantum evolution of two-level systems. Focusing on qubit dynamics on the Bloch sphere, we analyze evolutions generated by stationary and nonstationary Hamiltonians, corresponding to geodesic and nongeodesic trajectories. We formulate Krylov complexity in geometric terms, both instantaneously and in a time-averaged sense, and contrast it with an IG complexity of quantum evolutions characterized in terms of efficiency and curvature. We show that the two measures reflect fundamentally different aspects of quantum dynamics: Krylov's state complexity quantifies the directional spread of the evolving state relative to the initial state, whereas the IG complexity captures the effective volume explored along the trajectory on the Bloch sphere. This geometric distinction explains their inequivalent behavior and highlights the complementary nature of state-based and information-geometric notions of complexity in quantum systems. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.18941 [quant-ph] (or arXiv:2601.18941v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.18941 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Carlo Cafaro [view email] [v1] Mon, 26 Jan 2026 20:22:52 UTC (249 KB) Full-text links: Access Paper: View a PDF of the paper titled Krylov's State Complexity and Information Geometry in Qubit Dynamics, by Carlo Cafaro and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)