Predicting Magic from Very Few Measurements
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Quantum Physics arXiv:2602.18939 (quant-ph) [Submitted on 21 Feb 2026] Title:Predicting Magic from Very Few Measurements Authors:J. M. Varela, L. L. Keller, A. de Oliveira Junior, D. A. Moreira, R. Chaves, R. A. Macêdo View a PDF of the paper titled Predicting Magic from Very Few Measurements, by J. M. Varela and 5 other authors View PDF HTML (experimental) Abstract:The nonstabilizerness of quantum states is a necessary resource for universal quantum computation, yet its characterization is notoriously demanding. Quantifying nonstabilizerness typically requires an exponential number of measurements and a doubly exponential classical post-processing cost to evaluate its standard monotones. In this work, we show that nonstabilizerness is, to a large extent, in the eyes of the beholder: it can be witnessed and quantified using any set of $m$ $n$-qubit Pauli measurements, provided the set contains anti-commuting pairs. We introduce a general framework that projects the stabilizer polytope onto the subspace defined by these observables and provide an algorithm that estimates magic from Pauli expectation values with runtime exponential in the number of measurements $m$ and polynomial in the number of qubits $n$. By relating the problem to a stabilizer-restricted variant of the quantum marginal problem, we also prove that deciding membership in the corresponding reduced stabilizer polytope is NP-hard. In particular, unless $\mathrm{P} = \mathrm{NP}$, no algorithm polynomial in $m$ can solve the problem in full generality, thus establishing fundamental complexity-theoretic limitations. Finally, we employ our framework to compute nonstabilizerness in different Hamiltonian ground states, demonstrating the practical performance of our method in regimes beyond the reach of existing techniques. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2602.18939 [quant-ph] (or arXiv:2602.18939v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.18939 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Rafael Chaves [view email] [v1] Sat, 21 Feb 2026 19:13:43 UTC (562 KB) Full-text links: Access Paper: View a PDF of the paper titled Predicting Magic from Very Few Measurements, by J. M. Varela and 5 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 Change to browse by: cond-mat cond-mat.str-el 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?)