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Simulators can realise novel phenomena by separating them from thecomplexities of a full physical implementation. Here we put forward a schemethat can simulate the exotic statistics of $D(S_3)$ non-Abelian anyons withminimal resources. The qudit lattice representation of this planar codesupports local encoding of $D(S_3)$ anyons. As a proof-of-principledemonstration we employ a photonic simulator to encode a single qutrit andmanipulate it to perform the fusion and braiding properties of non-Abelian$D(S_3)$ anyons. The photonic technology allows us to perform the requirednon-unitary operations with much higher fidelity than what can be achieved withcurrent quantum computers. Our approach can be directly generalised to largersystems or to different anyonic models, thus enabling advances in theexploration of quantum error correction and fundamental physics alike.

Unveiling the non-Abelian statistics of $D(S_3)$ anyons via photonic simulation