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arXiv · 2510.15067

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

William Munizzi·Howard J. Schnitzer
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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.

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William Munizzi, Howard J. Schnitzer. 2025-10-16. Topological Preparation of Non-Stabilizer States and Clifford Evolution in $SU(2)_1$ Chern-Simons Theory. https://doi.org/10.1007/jhep09(2026)020

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