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

Abstract

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 present a protocol that manipulates the $Z_2$ fluxes (``visons''), and their bound Majorana zero mode, of the Kitaev model. This is achieved by adiabatically switching-off and -on interaction terms in the Hamiltonian, and applying a local magnetic field. We test our protocol by exchanging two Majorana zero modes, analysing the errors it produces. We find that the error rate of our protocol can be suppressed exponentially by increasing the adiabatic turn-on time and the size of the system. However, realistic implementations must consider the trade off between different error sources.