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

Demonstrating anyonic fractional statistics with a six-qubit quantum simulator