A Polylogarithmic-Depth Quantum Multiplier

Quantum Physics [Submitted on 10 Apr 2026] A Polylogarithmic-Depth Quantum Multiplier Fred Sun, Anton Borissov We present a quantum algorithm for multiplying two n-bit integers with overall circuit depth and T-depth both bounded by O(\log^{2} n), while using O(n^{2}) gates and ancillary qubits. Our construction generates partial products via indicator-controlled copying and adds them using a binary adder tree, enabling parallel accumulation with logarithmic depth overhead per level. To the best of our knowledge, our design has the lowest T-depth among all multiplication algorithms using the Clifford + T model. By optimizing both circuit depth and T-depth, our construction advances the practical feasibility of large-scale fault-tolerant quantum algorithms. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.09847 [quant-ph]   (or arXiv:2604.09847v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.09847 Focus to learn more Submission history From: Fred Sun [view email] [v1] Fri, 10 Apr 2026 19:21:07 UTC (64 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 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?)