Hidden Prime-Factor Subgroups in Molecular and Condensed-Phase Systems
Summarize this article with:
Quantum Physics arXiv:2605.04343 (quant-ph) [Submitted on 5 May 2026] Title:Hidden Prime-Factor Subgroups in Molecular and Condensed-Phase Systems Authors:Srinivasan S. Iyengar, Amr Sabry View a PDF of the paper titled Hidden Prime-Factor Subgroups in Molecular and Condensed-Phase Systems, by Srinivasan S. Iyengar and 1 other authors View PDF Abstract:We describe a group theoretic analysis of Shor's algorithm and other related hidden subgroup problems in mathematics and relate these to symmetries of molecular and condensed phase assemblies. By recasting Shor's algorithm through the lens of group theory, we expose the possibility that physical systems such as molecular orbitals, condensed phase assemblies and optical beams may be designed such that these contain information pertaining to the solution to hard mathematical problems such as prime-factoring. We discuss real molecular systems, whose orbitals are constructed from symmetry-adapted linear combinations of atomic orbitals, and show that these contain information pertaining to the prime-factors of corresponding integers. Due to the broad significance of prime-factoring towards a variety of encryption problems in cyber-security, we believe this novel and fundamental approach may have broad impact. Subjects: Quantum Physics (quant-ph); Group Theory (math.GR) Cite as: arXiv:2605.04343 [quant-ph] (or arXiv:2605.04343v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.04343 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Srinivasan Iyengar [view email] [v1] Tue, 5 May 2026 23:02:52 UTC (5,825 KB) Full-text links: Access Paper: View a PDF of the paper titled Hidden Prime-Factor Subgroups in Molecular and Condensed-Phase Systems, by Srinivasan S. Iyengar and 1 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: math math.GR 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?)