  We define creation and annihilation operators for any 2D non-abelian anyon
theory by studying the algebraic structure from the anyon diagrammatic
formalism. We construct the creation operators for Fibonacci anyons explicitly.
We obtain that a single creation operator per particle type is not enough; we
need an extra creation operator for every alternative fusion channel. We
express any physically allowed observable in terms of these creation and
annihilation operators. Finally, we express the 2D Fibonacci Hubbard
Hamiltonian in terms of the Fibonacci creation and annihilation operators, and
we comment on developing methods for simulation based on these creation and
annihilation operators.
