Zijian Song (Stony Brook): A potential method for logical gates via anyon permutations

Speaker: Zijian Song

Title: A potential method for logical gates via anyon permutations

Abstract: We construct explicit constant-depth local unitary circuits that realize general anyon permutations in Kitaev's quantum double models. This construction admits a natural interpretation in terms of a correspondence between anyon permutation symmetries of two-dimensional topological orders and self-dualities in one-dimensional systems. This approach also provides a practical route to implementing logical gates on topological quantum codes in constant depth.