Photonic simulation of parafermionic Berry-phase statistics and contextuality

2020 
Quasiparticle poisoning is the main obstacle towards the realization of Majorana-based quantum computation. Parafermions, a natural generalization of Majorana fermions, can encode topological qudits immune to quasiparticle poisoning. While parafermions are expected to emerge in superconducting fractional quantum Hall systems they are not yet attainable with current technology. To bypass this problem, we employ a photonic quantum simulator to experimentally demonstrate the key components of parafermion-based universal quantum computation. By manipulating the photonic states we realize Clifford operator Berry phases that correspond to parafermion braiding. Moreover, we demonstrate the contextuality of parafermion encoded qudit states that opens the way to magic state distillation. We finally establish the advantage parafermion qudits have against non-topological ones when they are exposed to local noise. Our photonic quantum simulation provides the first step towards a physically robust methodology for realizing topological quantum computation.
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