Twisted Interferometry: the topological perspective

Three manifold topology is used to analyze the effect of anyonic interferometers in which the probe anyons' path along an arm crosses itself, leading to a "twisted" or braided space-time trajectory for the probe anyons. In the case of Ising non-Abelian anyons, twisted interferometry is shown to be able to generate a topologically protected $π/8$-phase gate, which cannot be generated from quasiparticle braiding.

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