  Anyons are exotic quasiparticles living in two dimensions that do not fit
into the usual categories of fermions and bosons, but obey a new form of
fractional statistics. Following a recent proposal [Phys. Rev. Lett. 98, 150404
(2007)], we present an experimental demonstration of the fractional statistics
of anyons in the Kitaev spin lattice model using a photonic quantum simulator.
We dynamically create the ground state and excited states (which are six-qubit
graph states) of the Kitaev model Hamiltonian, and implement the anyonic
braiding and fusion operations by single-qubit rotations. A phase shift of
$\pi$ related to the anyon braiding is observed, confirming the prediction of
the fractional statistics of Abelian 1/2-anyons.
