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We study the effects of braiding interactions on single anyon dynamics usinga quantum walk model on a quasi-1-dimensional ladder filled with stationaryanyons. The model includes loss of information of the coin and nonlocal fusiondegrees of freedom on every second time step, such that the entanglementbetween the position states and the exponentially growing auxiliary degrees offreedom is lost. The computational complexity of numerical calculations reducesdrastically from the fully coherent anyonic quantum walk model, allowing forrelatively long simulations for anyons which are spin-1/2 irreps of SU(2)_kChern-Simons theory. We find that for Abelian anyons, the walk retains theballistic spreading velocity just like particles with trivial braidingstatistics. For non-Abelian anyons, the numerical results indicate that thespreading velocity is linearly dependent on the number of time steps. Byapproximating the Kraus generators of the time evolution map by circulantmatrices, it is shown that the spatial probability distribution for the k=2walk, corresponding to Ising model anyons, is equal to the classical unbiasedrandom walk distribution.

Quantum Walks of SU(2)_k Anyons on a Ladder