Formal Modeling and Verification of Grover's Algorithm

Quantum Physics arXiv:2601.02435 (quant-ph) [Submitted on 5 Jan 2026] Title:Formal Modeling and Verification of Grover's Algorithm Authors:H. Sun, Z. Shi, S. Chen, G. Wang, X. Li, Y. Guan, Q. Zhang, Z. Shao View a PDF of the paper titled Formal Modeling and Verification of Grover's Algorithm, by H. Sun and 7 other authors View PDF HTML (experimental) Abstract:Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum mechanics, the correctness of quantum algorithms is difficult to guarantee through traditional simulation methods. By contrast, the fundamental concepts and mathematical structure of Grover's algorithm can be formalized into logical expressions and verified by higher-order logical reasoning. In this paper, we formally model and verify Grover's algorithm in the HOL Light theorem prover. We focus on proving key properties such as the unitarity of its oracle and diffusion operators, the monotonicity of the success probability with respect to the number of iterations, and an exact expression for the optimal iteration count. By analyzing a concrete application to integer factorization, we demonstrate the practicality and prospects of our work. Comments: Subjects: Quantum Physics (quant-ph); Formal Languages and Automata Theory (cs.FL) ACM classes: F.4.3 Cite as: arXiv:2601.02435 [quant-ph] (or arXiv:2601.02435v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.02435 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Hongxia Sun [view email] [v1] Mon, 5 Jan 2026 06:56:21 UTC (2,008 KB) Full-text links: Access Paper: View a PDF of the paper titled Formal Modeling and Verification of Grover's Algorithm, by H. Sun and 7 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 Change to browse by: cs cs.FL 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?)