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