  The Kitaev quantum spin liquid possesses two fractional quasiparticles,
itinerant Majorana fermions and localized visons. It provides a promising
platform for realizing a Majorana zero mode trapped by a vison excitation. This
local mode behaves as a non-Abelian anyon capable of applications to quantum
computation. However, creating, observing, and manipulating visons remain
challenging even in the pristine Kitaev model. Here, we propose a theory to
control visons enabled by a time-dependent local magnetic field in the Kitaev
spin liquid. Examining the time evolution of the magnetic state, we demonstrate
that a vison follows a locally applied field sweeping in the system. We clarify
that one can move a vison accompanied by a Majorana zero mode by choosing the
velocity and shape of the local field appropriately. In particular, the
controllability of visons using local fields shows nonlinear behavior for its
strength, which originates from interactions between Majorana fermions and
visons. The present results suggest that itinerant Majorana fermions other than
zero modes play a crucial role in vison transport. Our finding will offer a
guideline for controlling Majorana zero modes in the Kitaev quantum spin
liquid.
