Graphical and algebraic methods for Boolean factoring
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Quantum Physics arXiv:2606.04038 (quant-ph) [Submitted on 2 Jun 2026] Title:Graphical and algebraic methods for Boolean factoring Authors:Simon Martiel, Priyanka Mukhopadhyay View a PDF of the paper titled Graphical and algebraic methods for Boolean factoring, by Simon Martiel and 1 other authors View PDF HTML (experimental) Abstract:The problem of factoring Boolean polynomials has significant applications in both classical and quantum computing technology. In this paper we have developed novel algorithms for factoring both ESOP and SOP expressions. Our aim is to optimize the AND-count. The AND-count plays a key role in determining the number of AND and Toffoli gates required to implement a reversible function with classical and quantum circuits, respectively. The first type of algorithms that we develop, are graphical. We reduce the problem of Boolean factoring to covering a bipartite graph with bicliques, and so optimizing the number of bicliques required to cover the bipartite graph, leads to reduced number of factors, and hence AND-count. The second type of algorithm is algebraic, and is derived from multivariate Horner method. We have compared the performances of our algorithms with existing popular methods like EXORCISM-4 and EPOEM2, on random functions of up to 12 variables. We have observed that our multivariate Horner method is substantially faster, while our biclique-based method achieves the maximum AND-count reduction. In fact, compared to EXORCISM-4 our biclique based method achieves up to 5 times reduction in AND-count. Subjects: Quantum Physics (quant-ph); Data Structures and Algorithms (cs.DS) Cite as: arXiv:2606.04038 [quant-ph] (or arXiv:2606.04038v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.04038 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Priyanka Mukhopadhyay Dr [view email] [v1] Tue, 2 Jun 2026 02:57:27 UTC (199 KB) Full-text links: Access Paper: View a PDF of the paper titled Graphical and algebraic methods for Boolean factoring, by Simon Martiel and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-06 Change to browse by: cs 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?)