τ×τ = 1+τ fusion rules; R and F matrices; topological quantum gates
Fusion state: |1⟩ |
Accumulated phase: 0.000 rad
Braid sequence: (empty)
Fibonacci anyons have two superselection sectors: 1 (vacuum) and τ. Fusion rule: τ⊗τ = 1⊕τ (golden ratio φ=(1+√5)/2 is the quantum dimension). R-matrix: R¹_ττ = e^{−4πi/5}, R^τ_ττ = e^{3πi/5}. F-matrix entries: F^τ_{ττ τ} with φ^{-1} and φ^{-1/2}. Braiding sequences of 4 anyons in the τ⊗τ→τ channel implement universal quantum gates — the key resource for topological quantum computing.