{"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/180304933","title":"Approximate Quantum Fourier Transform with $O(n \\log(n))$ T gates","arxiv_id":"1803.04933","date":"2018-03-13","proceeding":null,"authors":["Yunseong Nam","Yuan Su","Dmitri Maslov"],"abstract":"The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete logarithm over Abelian groups, solving systems of linear equations, and phase estimation, to name a few. The standard fault-tolerant implementation of an $n$-qubit unitary QFT approximates the desired transformation by removing small-angle controlled rotations and synthesizing the remaining ones into Clifford+T gates, incurring the T-count complexity of $O(n \\log^2(n))$. In this paper, we show how to obtain approximate QFT with the T-count of $O(n \\log(n))$. Our approach relies on quantum circuits with measurements and feedforward, and on reusing a special quantum state that induces the phase gradient transformation. We report asymptotic analysis as well as concrete circuits, demonstrating significant advantages in both theory and practice.","url_abs":"http://arxiv.org/abs/1803.04933v1","url_pdf":"http://arxiv.org/pdf/1803.04933v1.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":"180304933","repo_url":"https://github.com/y-nam/QFT","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}