Quantum magic in topological codes is harder to erase than expected

Some quantum states carry a property called "magic" (nonstabilizerness) that can't be removed by simple local operations — this is what makes quantum computers more powerful than classical ones. Using mutual information as a diagnostic, this work maps out which encoded states in 2D topological codes like the toric code retain long-range magic, and which logical gates can be implemented fault-tolerantly. The result tightly constrains what operations are achievable on a torus geometry without destroying the protected quantum information.