Topological Contextuality and Anyonic Statistics of Photonic-Encoded Parafermions

Quasiparticle poisoning, expected to arise during the measurement of Majorana zero mode state, poses a fundamental problem towards realization Majorana-based quantum computation. Parafermions, natural generalization fermions, can encode topological qudits immune quasiparticle poisoning. While parafermions are emerge in superconducting fractional Hall systems, they not yet attainable with current technology. To bypass this problem, we employ photonic simulator experimentally demonstrate key components parafermion-based universal Our contributions article twofold. First, by manipulating states, realize Clifford operator Berry phases that correspond braiding statistics parafermions. Second, investigate contextuality system for first time demonstrating parafermion encoded qudit states. Importantly, find topologically-encoded opens way magic state distillation, while both and braiding-induced gates resilient against local noise. By introducing contextuality, our simulation provides step physically robust methodology realizing