Learning Sparse Quantum States

Quantum Physics arXiv:2609.12219 (quant-ph) [Submitted on 10 Sep 2026] Title:Learning Sparse Quantum States Authors:Aniruddha Sen View a PDF of the paper titled Learning Sparse Quantum States, by Aniruddha Sen View PDF HTML (experimental) Abstract:We study the problem of tomography for $k$-sparse quantum states. In contrast to classical distribution learning, where tight sample and time complexity bounds in terms of support size are well understood, no non-trivial bounds were previously shown for this problem. We give the first near optimal algorithm for learning $n$-qubit $k$-sparse pure quantum states, obtaining fidelity at least $1-\varepsilon$ with high probability using $\tilde{O}(k/\varepsilon)$ copies of the state and $\tilde{O}(kn/\varepsilon)$ time. Both bounds are optimal up to polylogarithmic factors. As an implication, we also obtain an algorithm with near optimal $\tilde{O}(kr/\varepsilon)$ sample complexity for learning $k$-sparse rank-$r$ mixed states, via the random purification channel technique. Obtaining time complexity nearly matching the sample complexity, for $r>1$, remains an important open question. Comments: Subjects: Quantum Physics (quant-ph); Computational Complexity (cs.CC); Data Structures and Algorithms (cs.DS) Cite as: arXiv:2609.12219 [quant-ph] (or arXiv:2609.12219v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.12219 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Aniruddha Sen [view email] [v1] Thu, 10 Sep 2026 21:28:21 UTC (28 KB) Full-text links: Access Paper: View a PDF of the paper titled Learning Sparse Quantum States, by Aniruddha SenView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: cs cs.CC cs.DS 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?) 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?)