{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/revisiting-shor-s-quantum-algorithm-for","title":"Revisiting Shor's quantum algorithm for computing general discrete logarithms","arxiv_id":"1905.09084","date":"2019-05-22","proceeding":null,"authors":["Martin Ekerå"],"abstract":"We heuristically show that Shor's algorithm for computing general discrete logarithms achieves an expected success probability of approximately 60% to 82% in a single run when modified to enable efficient implementation with the semi-classical Fourier transform. By slightly increasing the number of group operations that are evaluated quantumly and performing a single limited search in the classical post-processing, or by performing two limited searches in the post-processing, we show how the algorithm can be further modified to achieve a success probability that heuristically exceeds 99% in a single run. We provide concrete heuristic estimates of the success probability of the modified algorithm, as a function of the group order $r$, the size of the search space in the classical post-processing, and the additional number of group operations evaluated quantumly. In the limit as $r \\rightarrow \\infty$, we heuristically show that the success probability tends to one. In analogy with our earlier works, we show how the modified quantum algorithm may be heuristically simulated classically when the logarithm $d$ and $r$ are both known. Furthermore, we heuristically show how slightly better tradeoffs may be achieved, compared to our earlier works, if $r$ is known when computing $d$. We generalize our heuristic to cover some of our earlier works, and compare it to the non-heuristic analyses in those works.","url_abs":"https://arxiv.org/abs/1905.09084v4","url_pdf":"https://arxiv.org/pdf/1905.09084v4.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"revisiting-shor-s-quantum-algorithm-for","repo_url":"https://github.com/ekera/qunundrum","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}