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In two-dimensions, the laws of physics even permit the existence of anyonswhich exhibit fractional statistics ranging continuously from bosonic tofermionic behaviour. They have been responsible for the fractional quantum Halleffect and proposed as candidates for naturally fault-tolerant quantumcomputation. Despite these remarkable properties, the fractional statistics ofanyons has never been observed in nature directly. Here we report thedemonstration of fractional statistics of anyons by simulation of the firstKitaev lattice-spin model on a nuclear magnetic resonance system. We encodefour-body interactions of the lattice-spin model into two-body interactions ofan Ising spin chain in molecules. It can thus efficiently prepare and operatethe ground state and excitations of the model Hamiltonian. This quantum systemwith convenience of manipulation and detection of abelian anyons revealsanyonic statistical properties distinctly. Our experiment with interactedHamiltonian could also prove useful in the long run to the control andapplication of anyons.

Experimental simulation of fractional statistics of abelian anyons in the Kitaev lattice-spin model