Topological Quantum Computing

Physics: Topological QC (Kitaev 1997): qubits encoded in global topological properties of anyon systems. Local perturbations cannot change topological quantum numbers → inherent decoherence protection. Braiding non-Abelian anyons implements unitary gates on the degenerate ground state. Fibonacci anyons: braiding alone is universal for QC. Fractional QHE ν=5/2: candidate non-Abelian anyons (Ising anyons, SU(2)_2 Chern-Simons theory). Microsoft hardware program: Majorana-based topological qubits. Gate error estimated <10⁻¹² — far better than superconducting or trapped ion approaches. Topology protects: gate outcome depends only on braid topology, not exact path.