Quantum simulation of lattice gauge theories coupled to fermionic matter via anyonic regularization

Quantum Physics [Submitted on 16 Mar 2026] Quantum simulation of lattice gauge theories coupled to fermionic matter via anyonic regularization Mason L. Rhodes, Shivesh Pathak, Riley W. Chien The optimal regularization of infinite-dimensional degrees of freedom is a central open problem in the tractable simulation of lattice gauge theories on quantum computers. Here, we consider regularizing the gauge field by replacing the gauge group G with a braided fusion category whose objects correspond to Wilson lines of the associated Chern-Simons theory G_k, with the level k serving as the regularization parameter. We demonstrate how to couple these regularized U(1) and SU(2) gauge groups to fermionic matter using the framework of fusion surface models, which treats matter and gauge field excitations as interacting anyons. We then address the simulation of the Hamiltonians we construct on fault-tolerant quantum computers, providing explicit quantum circuit constructions for implementing the primitive gates in this model, namely, the F and R symbols of the U(1)_k and SU(2)_k anyon theories, which may be of independent interest. Subjects: Quantum Physics (quant-ph); Strongly Correlated Electrons (cond-mat.str-el); High Energy Physics - Lattice (hep-lat) Cite as: arXiv:2603.15820 [quant-ph]   (or arXiv:2603.15820v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.15820 Focus to learn more Submission history From: Mason Rhodes [view email] [v1] Mon, 16 Mar 2026 18:51:41 UTC (502 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.str-el hep-lat References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)