Realizing general anyon permutation through constant-depth circuits

In this work, we present a general method for realizing anyon permutations in quantum double models through constant-depth circuits. This construction is rooted in the correspondence between dualities in one dimension and symmetries in two-dimensional topological orders. As illustrative examples, we explicitly discuss the circuits that realize all anyon permutations of the Z₂ x Z₂ toric code, as well as the generalized electric–magnetic permutations in the D_n quantum double models.