From Period Finding to Lattice Sampling: Experimental Insights into Shor's and Regev's Factoring Algorithms
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Quantum Physics arXiv:2606.17647 (quant-ph) [Submitted on 16 Jun 2026] Title:From Period Finding to Lattice Sampling: Experimental Insights into Shor's and Regev's Factoring Algorithms Authors:Daniela Falcó, Arturo Rodríguez, Guillermo Rivas, Ricardo S. Alonso View a PDF of the paper titled From Period Finding to Lattice Sampling: Experimental Insights into Shor's and Regev's Factoring Algorithms, by Daniela Falc\'o and Arturo Rodr\'iguez and Guillermo Rivas and Ricardo S. Alonso View PDF Abstract:Quantum algorithms for integer factorization represent one of the most prominent applications of quantum computation, with far-reaching implications for modern cryptography. While Shor's algorithm provides a polynomial-time solution in the ideal quantum model, its practical implementation is severely constrained by the limitations of current noisy intermediate-scale quantum (NISQ) hardware. These constraints have motivated the exploration of alternative factoring algorithms with different structural and resource trade-offs. In this work, we present an experimental study of Regev's quantum factoring algorithm, implemented on real quantum hardware, and compare its behavior with that of Shor's algorithm under analogous conditions. Focusing on the case N = 15, we execute both algorithms on the QMIO quantum computer at the Centro de Supercomputacion de Galicia (CESGA) and contrast the results with one of IBM's open-access quantum computers and ideal simulations. This parallel execution enables a low-level comparison of the two algorithms, highlighting how their respective quantum implementations interact with hardware noise, limited circuit depth, and finite sampling. Our analysis emphasizes the different ways in which Shor's and Regev's algorithms encode arithmetic structure into quantum states through Fourier sampling in one and higher dimensions, respectively, and how these differences manifest in experimental outcomes. Although neither algorithm demonstrates a practical advantage in the small N regime, the results provide insight into their relative robustness and failure modes on contemporary quantum devices. This study illustrates the value of experimental benchmarking of alternative quantum factoring algorithms as a means of understanding the practical implications of algorithmic design choices in the NISQ era. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2606.17647 [quant-ph] (or arXiv:2606.17647v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2606.17647 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Daniela Falcó [view email] [v1] Tue, 16 Jun 2026 08:06:38 UTC (612 KB) Full-text links: Access Paper: View a PDF of the paper titled From Period Finding to Lattice Sampling: Experimental Insights into Shor's and Regev's Factoring Algorithms, by Daniela Falc\'o and Arturo Rodr\'iguez and Guillermo Rivas and Ricardo S. AlonsoView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-06 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?)