Topological preparation of non-stabilizer states and Clifford evolution in SU(2)1 Chern-Simons theory

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Abstract
A bstract: 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. For the genus-1 case, the modular SL (2 , ℤ) generators on a single torus boundary realize the standard Clifford generators. We further conjecture a higher-genus extension of this correspondence specifically for the Clifford orbits of W and Dicke states, in which the orbit of W n is represented by a sum over genus- g handlebodies with Dehn twists applied to each torus. Our results extend the known correspondence between Clifford structures and modular transformations, and demonstrate that non-stabilizer states can be understood as controlled deformations within the SU (2) 1 modular tensor category, providing a concrete example of how non-stabilizer quantum resources emerge from purely topological data.

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