Planted-solution SAT and Ising benchmarks from integer factorization
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Quantum Physics arXiv:2604.09837 (quant-ph) [Submitted on 10 Apr 2026] Title:Planted-solution SAT and Ising benchmarks from integer factorization Authors:Itay Hen View a PDF of the paper titled Planted-solution SAT and Ising benchmarks from integer factorization, by Itay Hen View PDF HTML (experimental) Abstract:We present a family of planted-solution benchmark instances for satisfiability (SAT) solvers and Ising optimization derived from integer factorization. Given two primes $p$ and $q$, the construction encodes the arithmetic constraints of $N = p \times q$ as a conjunctive normal form (CNF) formula whose satisfying assignments correspond to valid factorizations of~$N$. The known pair $(p,q)$ serves as a built-in ground truth, enabling unambiguous verification of solver output. We show that for two $d$-bit primes the total number of carry contractions is on the order of $d^4$. Empirical benchmarks with SAT solvers show that median runtime grows exponentially in the bit-length of the factors over the range tested. The construction provides a scalable, structured, and verifiable benchmark family controlled by a single parameter, accompanied by open-source generation software. Comments: Subjects: Quantum Physics (quant-ph); Logic in Computer Science (cs.LO) Cite as: arXiv:2604.09837 [quant-ph] (or arXiv:2604.09837v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2604.09837 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Itay Hen [view email] [v1] Fri, 10 Apr 2026 19:09:24 UTC (173 KB) Full-text links: Access Paper: View a PDF of the paper titled Planted-solution SAT and Ising benchmarks from integer factorization, by Itay HenView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-04 Change to browse by: cs cs.LO 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?)