Improved quantum circuits for division

Quantum Physics [Submitted on 18 Mar 2026] Improved quantum circuits for division Priyanka Mukhopadhyay, Alexandru Gheorghiu, Hari Krovi Arithmetic operations are an important component of many quantum algorithms. As such, coming up with optimized quantum circuits for these operations leads to more efficient implementations of the corresponding algorithms. In this paper, we develop new fault-tolerant quantum circuits for various integer division algorithms (both reversible and non-reversible). These circuits, when implemented in the Clifford+T gate set, achieve an up to 76.08\% and 68.35\% reduction in T-count and CNOT-count, respectively, compared to previous circuit constructions. Some of our circuits also improve the asymptotic T-depth from O(n^2) to O(n \log n), where n is the bit-length of the dividend. The qubit counts are also lower than in previous works. We achieve this by expressing the division algorithms in terms of a primitive we call COMP-N-SUB, that compares two integers and conditionally subtracts them. We show that this primitive can be implemented at a cost, in terms of both Clifford and non-Clifford gates, that is comparable to one addition. This is in contrast to performing comparison and conditional subtraction separately, whose cost would be comparable to a controlled addition plus a regular addition. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.18110 [quant-ph]   (or arXiv:2603.18110v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.18110 Focus to learn more Submission history From: Priyanka Mukhopadhyay Dr [view email] [v1] Wed, 18 Mar 2026 13:41:43 UTC (38 KB) Access Paper: view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)