Twisted Interferometry: the topological perspective

TL;DR

This paper applies three manifold topology to analyze twisted anyonic interferometers, revealing their potential to generate topologically protected quantum gates, specifically a $rac{ ext{pi}}{8}$-phase gate for Ising anyons, beyond traditional braiding methods.

Contribution

It introduces a topological analysis of twisted interferometry, demonstrating its capability to produce quantum gates not achievable through standard quasiparticle braiding.

Findings

Twisted interferometry can generate a $rac{ ext{pi}}{8}$-phase gate for Ising anyons.

Topological protection of the phase gate is established.

The approach extends the toolkit for topological quantum computation.

Abstract

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 $\pi/8$-phase gate, which cannot be generated from quasiparticle braiding.