Protocol for coherently moving non-abelian anyons in quantum double models

Non-abelian topological quantum computation uses the internal states of non-abelian anyons to store logical information; computation is performed by braiding and fusion of non-abelian anyons. Therefore, the capability to coherently move non-abelian anyons is crucial. Existing protocols of coherently moving non-abelian anyons are involved and are only available as linear-depth circuits. We provide a more transparent general principle for constructing protocols to coherently move non-abelian anyons in quantum double models using the ribbon operator formalism. For solvable non-abelian quantum double models, the protocol allows one to take advantage of constant-depth adaptive circuit implementation of ribbon operators. We illustrate the theory with the simplest non-abelian quantum double model that allows for universal quantum computation: the quantum double of S3, the symmetry group of a triangle.