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

• URL: http://arxiv.org/abs/2510.15067v1
• Date: Thu, 16 Oct 2025 18:29:50 GMT
• Title: Topological Preparation of Non-Stabilizer States and Clifford Evolution in $SU(2)_1$ Chern-Simons Theory
• Authors: William Munizzi, Howard J. Schnitzer,
• Abstract summary: We develop a framework for preparing families of non-stabilizer states, and computing their entanglement entropies.<n>Using the Kac-Moody algebra, we construct Pauli and Clifford operators as path integrals over 3-manifolds with Wilson loop insertions.<n>Our results extend existing topological constructions for stabilizer states to include families of non-stabilizer states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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