Quantum walks on regular graphs with realizations in a system of anyons

We build interacting Fock spaces from association schemes and set up quantum walks on the resulting regular graphs (distance-regular distance-transitive). The construction is valid for growing space well defined asymptotically graph. To realize in terms of anyons we switch to dual view identify corresponding modular tensor categories Bose–Mesner algebra. Informally, fusion ring induced by scheme a topological twist can be basis developing category thus system anyons. Finally, demonstrate framework case Grover walk distance-regular graph anyon systems considered. In perspective gather new meaning collisions graphs.