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.
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