Braiding of quantum Hall quasiparticles. (Left) Adiabatic evolution of a quantum Hall wave function by moving one quasiparticle around another, returning to the original configuration. In fractional quantum Hall states, the result is sensitive to the sense of the “braid” shown (clockwise or anticlockwise). Braids of more than two quasiparticles are mathematically described by a “non-Abelian” group (they need not commute), and in non-Abelian quantum Hall states, the action of braids on the space of wave functions is given by matrices that do not commute. (Right) Sketch of an experimental interferometer with a gate P that effectively moves edge quasiparticles (blue) around bulk quasiparticles (light gray); the total conductance through the point contacts (dark gray) is sensitive to quasiparticle statistics.