  In recent years, there has been an intense search for materials realizing the
Kitaev quantum spin liquid model. A number of edge-shared compounds with strong
spin-orbit coupling, such as RuCl$_3$ and iridates, have been proposed to
realize this model. Nevertheless, an effective spin Hamiltonian derived from
the microscopic model relevant to these compounds generally contains terms that
are antagonistic toward the quantum spin liquid. This is consistent with the
fact the zero magnetic field ground state of these materials is generally
magnetically ordered. It is a pressing issue to identify protocols to drive the
system to the limit of the Kitaev quantum spin model. In this work, we propose
Floquet engineering of these Kitaev quantum magnets by coupling materials to a
circularly polarized laser. We demonstrate that all the magnetic interactions
can be tuned in situ by the amplitude and frequency of the laser, hence
providing a route to stabilize the Kitaev quantum spin liquid phase.
