  Interacting systems of anyons pose a unique challenge to condensed matter
simulations due to their non-trivial exchange statistics. These systems are of
great interest as they have the potential for robust universal quantum
computation, but numerical tools for studying them are as yet limited. We show
how existing tensor network algorithms may be adapted for use with systems of
anyons, and demonstrate this process for the 1-D Multi-scale Entanglement
Renormalisation Ansatz (MERA). We apply the MERA to infinite chains of
interacting Fibonacci anyons, computing their scaling dimensions and local
scaling operators. The scaling dimensions obtained are seen to be in agreement
with conformal field theory. The techniques developed are applicable to any
tensor network algorithm, and the ability to adapt these ansaetze for use on
anyonic systems opens the door for numerical simulation of large systems of
free and interacting anyons in one and two dimensions.
