Extremely slow scaling of minimal Hamming distance in quantum sampling data
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Quantum Physics arXiv:2606.04558 (quant-ph) [Submitted on 3 Jun 2026] Title:Extremely slow scaling of minimal Hamming distance in quantum sampling data Authors:P. S. Golubev, I. A. Iakovlev, V. V. Mazurenko View a PDF of the paper titled Extremely slow scaling of minimal Hamming distance in quantum sampling data, by P. S. Golubev and 2 other authors View PDF HTML (experimental) Abstract:Quantum data can be obtained from a diverse range of sources, including direct measurements from noisy quantum processors, cold-atom simulators, and classical approximations such as variational neural-network states. However, our ability to characterize these systems is fundamentally limited, as the available measurement data is often sparse compared to the exponentially large Hilbert space of the system. To address this, we propose using the average minimal Hamming distance calculated for a set of unique bitstrings as a robust metric revealing a universal power-law behaviour. Through various examples of real experiments and simulations, we show that the power-law parameters reliably capture the complexity of quantum states and identify quantum phase transitions from limited quantum information, without the need for accumulating extensive statistics or explicitly calculating physical observables. This enables the analysis of completely different quantum experiments within a single framework. Subjects: Quantum Physics (quant-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2606.04558 [quant-ph] (or arXiv:2606.04558v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.04558 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Vladimir Mazurenko Dr. [view email] [v1] Wed, 3 Jun 2026 07:43:12 UTC (731 KB) Full-text links: Access Paper: View a PDF of the paper titled Extremely slow scaling of minimal Hamming distance in quantum sampling data, by P. S. Golubev and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cond-mat cond-mat.dis-nn 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?) 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?)