Creation operators for 2+1 non-abelian anyons

Topological quantum computing has been a fruitful area of research in recent times. The diagrammatic formalism of 2+1 D non-abelian anyons is the framework where topological quantum computation is formulated.

In this talk I will show how to find the annihilation operators for any non-abelian anyon theory in 2+1 D, modifying the diagrammatic formalism. Moreover, I analyse the algebraic relations of the anyonic creation and annihilation operators. I show how the number of creation operators is related to the number of different allowed fusion channels. I specifically show the cases of Fibonacci anyons and Majorana fermions. I explore some possible uses of these new structures, as studying the 2D anyonic Hubbard model via a generalised anyonic Jordan-Wigner transformation or opening new avenues for error correcting codes for quasiparticle poisoning.