An Error Correctable Implication Algebra for a System of Qubits

Quantum Physics arXiv:2511.14797 (quant-ph) [Submitted on 16 Nov 2025] Title:An Error Correctable Implication Algebra for a System of Qubits Authors:Morrison Turnansky View a PDF of the paper titled An Error Correctable Implication Algebra for a System of Qubits, by Morrison Turnansky View PDF HTML (experimental) Abstract:We present the Lukasiewicz logic as a viable system for an implication algebra on a system of qubits. Our results show that the three valued Lukasiewicz logic can be embedded in the stabilized space of an arbitrary quantum error correcting stabilizer code. We then fully characterize the non trivial errors that may occur up to group isomorphism. Lastly, we demonstrate by explicit algorithmic example, how any algorithm consistent with the Lukasiewicz logic can immediately run on a quantum system and utilize the indeterminate state. Subjects: Quantum Physics (quant-ph); Mathematical Physics (math-ph) MSC classes: 81P68, 94B05, 81R15, 46L60, 06B15 ACM classes: F.4.1 Cite as: arXiv:2511.14797 [quant-ph] (or arXiv:2511.14797v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.14797 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Morrison Turnansky [view email] [v1] Sun, 16 Nov 2025 20:35:44 UTC (18 KB) Full-text links: Access Paper: View a PDF of the paper titled An Error Correctable Implication Algebra for a System of Qubits, by Morrison TurnanskyView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 Change to browse by: math math-ph math.MP 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?)