Non-Clifford quantum cellular automata from invertible topological quantum field theories

Quantum Physics arXiv:2607.21697 (quant-ph) [Submitted on 23 Jul 2026] Title:Non-Clifford quantum cellular automata from invertible topological quantum field theories Authors:Meng Sun, Zongyuan Wang, Bowen Yang, Nathanan Tantivasadakarn, Yu-An Chen View a PDF of the paper titled Non-Clifford quantum cellular automata from invertible topological quantum field theories, by Meng Sun and 4 other authors View PDF Abstract:Quantum cellular automata (QCAs) describe locality-preserving quantum dynamics and connect quantum information, many-body physics, and topological quantum field theory (TQFT). Constructing a QCA from a TQFT, however, is challenging. Although a topological action can produce a commuting Hamiltonian realizing the desired ground state, it does not by itself specify an automorphism of the full local operator algebra. In this work, we develop a unified algebraic construction that extends the commuting generators of the Hamiltonian to a complete separator-flipper algebra on the full tensor-product Hilbert space, providing a microscopic definition of the corresponding QCA. In three spatial dimensions, our formalism unifies all previously known QCA constructions associated with the $\mathbb Z_8\times\mathbb Z_2$ subgroup of the Witt group, including the $U(1)_2$ and $U(1)_4$ QCAs. The same algebraic structure directly yields new infinite families of generalized $U(1)_2$ and $U(1)_4$ non-Clifford QCAs in dimensions $d=4k-1$. We also reformulate the 4-dimensional $w_2w_3$ QCA and use it to develop a general construction of QCAs from TQFTs associated with arbitrary products of Wu classes. This construction includes two infinite families. The first consists of $w_2^nw_3^m$ QCAs in dimension $d=2n+3m-1$, while the second consists of $w_2w_{4k-1}$ QCAs in dimension $d=4k$. As a contrasting result, we explicitly construct finite-depth quantum circuits for the 5-dimensional $w_3^2$ and $w_2^3$ QCAs, thereby proving that they are trivial, in agreement with the cobordism classification. Overall, these results convert invertible TQFTs into microscopic QCAs, provide a scalable route to higher-dimensional constructions beyond the Clifford setting, and open a systematic approach to classifying their stable structures and boundary anomalies. Comments: Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph); Quantum Algebra (math.QA) Cite as: arXiv:2607.21697 [quant-ph] (or arXiv:2607.21697v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.21697 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nathanan Tantivasadakarn [view email] [v1] Thu, 23 Jul 2026 18:00:00 UTC (121 KB) Full-text links: Access Paper: View a PDF of the paper titled Non-Clifford quantum cellular automata from invertible topological quantum field theories, by Meng Sun and 4 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: cond-mat cond-mat.str-el hep-th math math-ph math.MP math.QA 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?)