Braiding of non-Abelian anyons using pairwise interactions

The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange (braiding) operators of anyons by adiabatically varying pairwise interactions between them rather than their positions. We analyze a system composed by four anyons whose couplings define a T junction, and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains in order to recover the topological protection.