Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers

Quantum Physics arXiv:2510.20145 (quant-ph) [Submitted on 23 Oct 2025] Title:Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers Authors:José E. Cruz Serrallés, Oluwadara Ogunkoya, Do{g}a Murat Kürkçüo{g}lu, Nicholas Bornman, Norm M. Tubman, Anna Grassellino, Silvia Zorzetti, Riccardo Lattanzi View a PDF of the paper titled Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers, by Jos\'e E. Cruz Serrall\'es and 7 other authors View PDF Abstract:We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our proposed approach to develop quantum algorithms for fundamental arithmetic operations, such as bit-shifting, reciprocation, multiplication, and addition. We prototyped and investigated the performance of the floating-point encoding scheme on quantum computer simulations by performing reciprocation on randomly drawn inputs and by solving first-order ordinary differential equations, while varying the number of qubits in the encoding. We observed rapid convergence to the exact solutions as we increased the number of qubits and a significant reduction in the number of ancilla qubits required for reciprocation when compared with similar approaches. Subjects: Quantum Physics (quant-ph) Report number: FERMILAB-PUB-25-0270-SQMS Cite as: arXiv:2510.20145 [quant-ph] (or arXiv:2510.20145v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.20145 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Doga Kurkcuoglu [view email] [v1] Thu, 23 Oct 2025 02:45:41 UTC (175 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Floating-Point Arithmetic on Fault-Tolerant Quantum Computers, by Jos\'e E. Cruz Serrall\'es and 7 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-10 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?)