Anyons are 2D quasiparticles with fractional statistics — neither bosons nor fermions. When anyon worldlines braid, the quantum state acquires a unitary matrix (not just a phase). Fibonacci anyons (τ): fusion rule τ×τ = 1 + τ. The 2D space of four-anyon fusions carries a braid group representation. σ₁ → R-matrix, σ₂ → F⁻¹RF. Any SU(2) rotation can be approximated by braids (topological universality). Topological protection: the gate depends only on the topology of the braid, not on timing or position — intrinsically fault-tolerant. Ising anyons (σ): σ×σ = 1 + ψ. Braiding generates Clifford gates; requires magic state distillation for universality.