Anyon Permutations in Quantum Double Models through Constant-depth Circuits

• URL: http://arxiv.org/abs/2602.10110v1
• Date: Tue, 10 Feb 2026 18:59:23 GMT
• Title: Anyon Permutations in Quantum Double Models through Constant-depth Circuits
• Abstract summary: Local unitary circuits realize general anyon permutations in Kitaev's quantum double models.<n>General anyon permutations in the $D(G)$ quantum double correspond to compositions of three classes of one-dimensional self-dualities.
• Score: 2.346861719426151
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We provide explicit constant-depth local unitary circuits that realize general anyon permutations in Kitaev's quantum double models. This construction can be naturally understood through a correspondence between anyon permutation symmetries of two-dimensional topological orders and self-dualities in one-dimensional systems, where local gates implement self-duality transformations on the boundaries of microscopic regions. From this holographic perspective, general anyon permutations in the $D(G)$ quantum double correspond to compositions of three classes of one-dimensional self-dualities, including gauging of certain subgroups of $G$, stacking with $G$ symmetry-protected topological phases, and outer automorphisms of the group $G$. We construct circuits realizing the first class by employing self-dual unitary gauging maps, and present transversal circuits for the latter two classes.

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