Non-Abelian braiding and encoded gates
Exchanging non-Abelian anyons can rotate a protected degenerate subspace.
$$U_{ij}=\exp\!\left(\frac{\pi}{4}\gamma_i\gamma_j\right)$$
What this means
Exchanging non-Abelian anyons can rotate a protected degenerate subspace.
Deep dive: mathematical and physical mechanism
For ideal Ising/Majorana anyons, exchanging adjacent Majoranas implements $U_{ij}$ up to orientation and phase convention. Gates depend on braid topology rather than fine details of paths, provided adiabaticity and separation hold.
How it appears in quantum phenomena
Topological quantum computing proposals encode information in fusion spaces.
Assumptions, caveats and limitations
Braiding Ising anyons alone is not computationally universal; additional resources are needed.
Connect the ideas
For context, see the Interacting Topological Phases topic guide and the reading references.