Enhancing the Practical Reliability of Shor's Quantum Algorithm via Generalized Period Decomposition: Theory and Large-Scale Empirical Validation
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Quantum Physics arXiv:2512.11004 (quant-ph) [Submitted on 11 Dec 2025] Title:Enhancing the Practical Reliability of Shor's Quantum Algorithm via Generalized Period Decomposition: Theory and Large-Scale Empirical Validation Authors:Chih-Chen Liao, Chia-Hsin Liu, Yun-Cheng Tsai View a PDF of the paper titled Enhancing the Practical Reliability of Shor's Quantum Algorithm via Generalized Period Decomposition: Theory and Large-Scale Empirical Validation, by Chih-Chen Liao and Chia-Hsin Liu and Yun-Cheng Tsai View PDF HTML (experimental) Abstract:This work presents a generalized period decomposition approach, significantly improving the practical reliability of Shor's quantum factoring algorithm. Although Shor's algorithm theoretically enables polynomial-time integer factorization, its real-world performance heavily depends on stringent conditions related to the period obtained via quantum phase estimation. Our generalized decomposition method relaxes these conditions by systematically exploiting arbitrary divisors of the obtained period, effectively broadening the applicability of each quantum execution. Extensive classical simulations were performed to empirically validate our approach, involving over one million test cases across integers ranging from 2 to 8 digits. The proposed method achieved near-perfect success rates, exceeding 99.998% for 7-digit numbers and 99.999% for 8-digit numbers, significantly surpassing traditional and recently improved variants of Shor's algorithm. Crucially, this improvement is achieved without compromising the algorithm's polynomial-time complexity and integrates seamlessly with existing quantum computational frameworks. Moreover, our method enhances the efficiency of quantum resource usage by minimizing unnecessary repetitions, making it particularly relevant for quantum cryptanalysis with noisy intermediate-scale quantum (NISQ) devices. This study thus provides both theoretical advancements and substantial practical benefits, contributing meaningfully to the field of quantum algorithm research and the broader field of quantum information processing. Subjects: Quantum Physics (quant-ph); Cryptography and Security (cs.CR) Cite as: arXiv:2512.11004 [quant-ph] (or arXiv:2512.11004v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.11004 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Yun-Cheng Tsai [view email] [v1] Thu, 11 Dec 2025 00:06:25 UTC (1,711 KB) Full-text links: Access Paper: View a PDF of the paper titled Enhancing the Practical Reliability of Shor's Quantum Algorithm via Generalized Period Decomposition: Theory and Large-Scale Empirical Validation, by Chih-Chen Liao and Chia-Hsin Liu and Yun-Cheng TsaiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.CR 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?)