Topological Preparation of Non-Stabilizer States and Clifford Evolution in $SU(2)_1$ Chern-Simons Theory

Abstract:We develop a topological framework for preparing families of non-stabilizer states, and computing their entanglement entropies, in $SU(2)_1$ Chern-Simons theory. Using the Kac-Moody algebra, we construct Pauli and Clifford operators as path integrals over 3-manifolds with Wilson loop insertions, enabling an explicit topological realization of $W_n$ and Dicke states, as well as their entanglement properties. We further establish a correspondence between Clifford group action and modular transformations generated by Dehn twists on genus-$g$ surfaces, linking the mapping class group to quantum operations. Our results extend existing topological constructions for stabilizer states to include families of non-stabilizer states, improving the geometric interpretation of entanglement and quantum resources in topological quantum field theory.

arXiv:2510.15067 [hep-th]

(or arXiv:2510.15067v3 [hep-th] for this version)

https://doi.org/10.48550/arXiv.2510.15067 Focus to learn more arXiv-issued DOI via DataCite

https://doi.org/10.1007/JHEP09%282026%29020 Focus to learn more DOI(s) linking to related resources

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