Manipulating non-Abelian anyons of Kitaev quantum spin liquids with local magnetic fields

Non-Abelian anyonic excitations of quantum spin liquids have potential for application to topological quantum computation, but designing logical operations requires developing protocols to faithfully create, move, and read out such quasiparticles. In this paper, we test two such protocols for manipulating <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>Z</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> fluxes (“visons”) of ferromagnetic and antiferromagnetic Kitaev models perturbed by a small uniform magnetic field. We show that a protocol that employs a driving magnetic field locally applied to the sites of the lattice suffers from significant unavoidable errors. These errors, accumulating over time, prevent reaching high probabilities of generating and displacing flux pairs. However, individual spin couplings can also be turned on and off, thus it is possible to create and displace fluxes with nearly <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mrow> <b:mn>100</b:mn> <b:mo>%</b:mo> </b:mrow> </b:math> probability. We show that braiding non-Abelian anyons can be achieved with good precision with our second protocol. We comment on the feasibility of our protocols in solid-state devices and quantum emulators.