Topological Quantum Computation from non-abelian ... - Paul Fendley

To find a quantum loop model which has Fibonacci anyons, one needs to overcomeseveral technical obstacles: the d = √ 2 barrier, and finding a topological inner product.These both end up being solved by allowing “loops” to branch, so the degrees of freedomare best called nets.A very exciting mathematical byproduct is that using quantum topology we find newalgebraic proofs of the golden identity for the chromatic polynomial. We also find manygeneralizations.33