Non-Abelian anyons carry a form of complexity stabilizer circuits can never fake

Magic — the resource that makes quantum states hard to simulate classically — turns out to be deeply tied to the structure of non-Abelian topological order. A no-go theorem proves that stabilizer states cannot approximate the low-energy states of non-Abelian string-net models, even after applying a constant-depth local unitary. For Abelian phases, the paper identifies a precise braiding-phase condition whose violation forces extensive long-range magic. The result extends to higher dimensions: any area-law state hosting excitations with nontrivial fusion spaces must carry this irreducible complexity, sharpening how topological orders are classified as quantum resources.