Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions

Quantum Physics arXiv:2609.30285 (quant-ph) [Submitted on 3 Sep 2026] Title:Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions Authors:Dogukan Bakircioglu, Pablo Arrighi View a PDF of the paper titled Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions, by Dogukan Bakircioglu and Pablo Arrighi View PDF HTML (experimental) Abstract:This work provides a digital quantum simulation scheme for $1{+}1$-dimensional $SU(2)$ Yang--Mills theory with Dirac fermions. It takes the form of a quantum circuit, infinitely repeating across space and time with $\Delta_t=\Delta_x=\varepsilon$, whose wires follow lightlike propagation. The construction mirrors the logic of the standard quantum field theory approach, transposed to the discrete setting. Namely, we start from the Dirac quantum walk, restore $SU(2)$ gauge symmetry by introducing the gauge field, lift the walk to a multi-particle QCA while preserving fermionic anticommutation, and equip the gauge field with its own dynamics. Rather than relying on Clebsch--Gordan decompositions, we use the pointwise-product structure of gauge-link updates, which yields self-contained proofs of unitarity and gauge covariance in quantum-computing notation. The construction provides an explicit algorithmic formulation of the theory, whose continuum limit we discuss. Subjects: Quantum Physics (quant-ph); High Energy Physics - Lattice (hep-lat) Cite as: arXiv:2609.30285 [quant-ph] (or arXiv:2609.30285v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.30285 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Dogukan Bakircioglu [view email] [v1] Thu, 3 Sep 2026 19:10:11 UTC (41 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-abelian quantum cellular automata: $1{+}1$-dimensional $SU(2)$ Yang--Mills with fermions, by Dogukan Bakircioglu and Pablo ArrighiView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 Change to browse by: hep-lat 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?)