Topological contextuality and anyonic statistics of photonic-encoded parafermions

TL;DR

This paper uses photonic quantum simulation to demonstrate key aspects of parafermion-based topological quantum computation, including braiding statistics and quantum contextuality, highlighting their robustness and potential for fault-tolerant quantum computing.

Contribution

It experimentally demonstrates parafermion braiding and contextuality using photonic states, advancing topological quantum computation research.

Findings

Realized Clifford operator Berry phases for parafermion braiding.

Demonstrated quantum contextuality in a topological system.

Showed resilience of topological features against local noise.

Abstract

Quasiparticle poisoning, expected to arise during the measurement of Majorana zero mode state, poses a fundamental problem 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. Our contributions in this article are twofold. First, by manipulating the photonic states, we realize Clifford operator Berry phases that correspond to braiding statistics of parafermions. Second, we investigate the quantum contextuality in a topological system for the first time by demonstrating the contextuality of parafermion encoded qudit states. Importantly, we find that the topologically-encoded contextuality opens the way to magic state distillation, while both the contextuality and the braiding-induced Clifford gates are resilient against local noise. By introducing contextuality, our photonic quantum simulation provides the first step towards a physically robust methodology for realizing topological quantum computation.