Extended Data Fig. 4: The process described by \({\mathbf{B}}_{\mathbf{p}}^{\mathbf{s}}\) as a closed string operator.
From: Non-Abelian braiding of Fibonacci anyons with a superconducting processor
The effect of \({B}_{p}^{s}\) can be understood as creating a pair of type-s excitations from vacuum, moving the excitations around this plaquette, and annihilating them to vacuum. Under the tailed string-net picture, the positions of the tails clearly reveal this process. In this figure, we only move the tail initialized on the left. However, different schemes of moving these tails along this path do not change the algebraic representation of the closed string operator \({B}_{p}^{s}\) according to Mac Lane’s coherence theorem52.
