Geometric Stabilization of Non-Abelian Braids Under Noise via the Geometric Schrodinger Equation

We present a numerical investigation of non-Abelian braid execution under stochastic perturbations using the Geometric Schrodinger Equation (GSE). Unlike conventional topological quantum computing approaches that rely on abstract braid equivalence and idealized adiabatic assumptions, the GSE introduces a deterministic geometric flow with an auxiliary stabilization channel. We demonstrate that braid execution can be realized as a dynamically attracting process rather than a fragile path-following procedure. Using an explicit braid word and continuous noise injection, we show bounded planar phase motion and exponential convergence in the lift dimension. These results indicate that topological equivalence can emerge as a geometric attractor, providing a control-theoretic foundation for robust braid execution in realistic noisy environments.