Unveiling the Non-Abelian Statistics of D(S_{3}) Anyons Using a Classical Photonic Simulator

Simulators can realize novel phenomena by separating them from the complexities of a full physical implementation. Here, we put forward a scheme that can simulate the exotic statistics of D(S_{3}) non-Abelian anyons with minimal resources. The qudit lattice representation of this planar code supports local encoding of D(S_{3}) anyons. As a proof-of-principle demonstration, we employ a classical photonic simulator to encode a single qutrit and manipulate it to perform the fusion and braiding properties of non-Abelian D(S_{3}) anyons. The photonic technology allows us to perform the required nonunitary operations with much higher fidelity than what can be achieved with current quantum computers. Our approach can be directly generalized to larger systems or to different anyonic models, thus enabling advances in the exploration of quantum error correction and fundamental physics alike.