Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition

Quantum Physics arXiv:2609.28882 (quant-ph) [Submitted on 24 Sep 2026] Title:Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition Authors:Jieyi Long, Theodore Pender, Zhao Huang, Manuel B. Santos, Samrendra Kumar Singh, Bartosz Naskręcki, BitWonka, Pierre-Luc Dallaire-Demers, Francesco Giannicola, Ruben M. L. Paschoarelli, Oli Freuler, Jackie Chia-Hsun Lee, Vasily Gnuchev, Gopi Kannappan, John Boyer, Xavier Butler, Akash Balasubramani, Jordan Newman, Bereket Dereje, Alexander Hertlein, Robert Kodra, Lucas Levy, Shaan Patel, JT Rose, Matt Zweil, Okechukwu Wisdom, Tarek El-Eter, Edison Lee, Michael Dong, Alan Li, Anto Joseph, Duy Nguyen, Gajesh Naik, Gautham Anant, Soubhik Deb, Justin Drake View a PDF of the paper titled Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition, by Jieyi Long and 35 other authors View PDF HTML (experimental) Abstract:We study reversible secp256k1 point-addition circuits developed through this http URL for Shor's elliptic-curve discrete-logarithm algorithm. Two complementary constructions improve record-and-replay GCD arithmetic: Jump-2 groups binary-GCD steps and compresses their decisions using base-5 encoding, while ping-pong uses fixed register alternation and one-bit decisions to avoid full-width comparisons and data-dependent swaps. Fused replay combines doubling and signed addition into one modular correction. Both constructions support quantum-addressed window selection with measurement-based lookup cleanup. We compare three circuits on 100,000 fresh inputs across nine lookup-table configurations. A separately tested repair uses 1,419 qubits and 1.356 million mean executed Toffolis, with no detected failures on another 100,000 inputs. Structured supported-input counterexamples remain, so these tests do not establish all-input correctness. We also provide conditional coherent-error analysis and reversible safegcd comparisons. Under the stated window allowance, repaired-circuit resources lie below Google's low-gate caps and Schrottenloher's low-gate estimates, but differing accounting and correctness evidence preclude formal dominance. The results concern individual window-selected additions, not complete Shor computations. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.28882 [quant-ph] (or arXiv:2609.28882v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.28882 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Jieyi Long [view email] [v1] Thu, 24 Sep 2026 00:59:32 UTC (80 KB) Full-text links: Access Paper: View a PDF of the paper titled Efficient Record-and-Replay Arithmetic for Quantum Elliptic-Curve Point Addition, by Jieyi Long and 35 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?) 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?)