The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic
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Quantum Physics arXiv:2512.12073 (quant-ph) [Submitted on 12 Dec 2025] Title:The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic Authors:G. Papakonstantinou View a PDF of the paper titled The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic, by G. Papakonstantinou View PDF HTML (experimental) Abstract:Efficient arithmetic operations are a prerequisite for practical quantum computing. Optimization efforts focus on two primary metrics: Quantum Cost (QC), determined by the number of non-linear gates, and Logical Depth, which defines the execution speed. Existing literature identifies the HNG gate as the standard for Input-Preserving Reversible Full Adders. HNG gate typically requires a QC of 12 and a logical depth of 5, in the area of classical reversible circuits. This paper proposes the PPKN Gate, a novel design that achieves the same inputpreserving functionality using only one Toffoli gate and five CNOT gates. With a Quantum Cost of 10 and a reduced logical depth of 4, the PPKN gate outperforms the standard HNG gate in both complexity and speed. Furthermore, we present a modular architecture for constructing an n-bit Ripple Carry Adder by cascading PPKN modules. Subjects: Quantum Physics (quant-ph); Emerging Technologies (cs.ET) Cite as: arXiv:2512.12073 [quant-ph] (or arXiv:2512.12073v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.12073 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: George Papakonstantinou [view email] [v1] Fri, 12 Dec 2025 22:41:49 UTC (4 KB) Full-text links: Access Paper: View a PDF of the paper titled The PPKN Gate: An Optimal 1-Toffoli Input-Preserving Full Adder for Quantum Arithmetic, by G. PapakonstantinouView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-12 Change to browse by: cs cs.ET 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?)