Geometry of Quantum Logic Gates

Quantum Physics arXiv:2602.15080 (quant-ph) [Submitted on 16 Feb 2026] Title:Geometry of Quantum Logic Gates Authors:M. W. AlMasri View a PDF of the paper titled Geometry of Quantum Logic Gates, by M. W. AlMasri View PDF HTML (experimental) Abstract:In this work, we investigate the geometry of quantum logic gates within the holomorphic representation of quantum mechanics. We begin by embedding the physical qubit subspace into the space of holomorphic functions that are homogeneous of degree one in each Schwinger boson pair $(z_{a_{j}}, z_{b_{j}})$. Within this framework, we derive explicit closed-form differential operator representations for a universal set of quantum gates--including the Pauli operators, Hadamard, CNOT, CZ, and SWAP--and demonstrate that they preserve the physical subspace exactly. Restricting to unit-magnitude variables ($|z| = 1$) reveals a toroidal space $\mathbb{T}^{2N}$, on which quantum gates act as canonical transformations: Pauli operators generate Hamiltonian flows, the Hadamard gate induces a nonlinear automorphism, and entangling gates produce correlated diffeomorphisms that couple distinct toroidal factors. Beyond the torus, the full Segal--Bargmann space carries a natural Kaehler geometry that governs amplitude dynamics. Entanglement is geometrically characterized via the Segre embedding into complex projective space, while topological protection arises from the $U(1)^{N}$ fiber bundle structure associated with the Jordan--Schwinger constraint. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2602.15080 [quant-ph] (or arXiv:2602.15080v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2602.15080 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Mohammad Walid AlMasri [view email] [v1] Mon, 16 Feb 2026 09:21:53 UTC (13 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometry of Quantum Logic Gates, by M. W. AlMasriView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-02 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?)