Coauthors: Gavin Brennen

Quantum walks are coherent adaptations of Markovian random walks to quantum mechanical dynamics and they exhibit dynamics not found in classical walks (e.g. quadratic vs. linear dispersion). In this talk, the quantum walk scheme with anyons is introduced. Anyons are point like particles in two dimensions which can have an arbitrary phase under exchange in the Abelian case or a matrix valued action on the Hilbert space of fusion outcomes in the non-Abelian case. The non-trivial action under exchange acts as source of non-local decoherence on the anyonic walker. Simulations and analytical results for the walk on a disk and on an annulus are presented and the properties of anyon walks are compared to those of Markov walks and discrete quantum walks.