  In two-dimensions, the laws of physics even permit the existence of anyons
which exhibit fractional statistics ranging continuously from bosonic to
fermionic behaviour. They have been responsible for the fractional quantum Hall
effect and proposed as candidates for naturally fault-tolerant quantum
computation. Despite these remarkable properties, the fractional statistics of
anyons has never been observed in nature directly. Here we report the
demonstration of fractional statistics of anyons by simulation of the first
Kitaev lattice-spin model on a nuclear magnetic resonance system. We encode
four-body interactions of the lattice-spin model into two-body interactions of
an Ising spin chain in molecules. It can thus efficiently prepare and operate
the ground state and excitations of the model Hamiltonian. This quantum system
with convenience of manipulation and detection of abelian anyons reveals
anyonic statistical properties distinctly. Our experiment with interacted
Hamiltonian could also prove useful in the long run to the control and
application of anyons.
