  The aim of presented research is to design a nanodevice, based on a MoS$_2$
monolayer, performing operations on a well-defined valley qubit. We show how to
confine an electron in a gate induced quantum dot within the monolayer, and to
perform the NOT operation on its valley degree of freedom. The operations are
carried out all electrically via modulation of the confinement potential by
oscillating voltages applied to the local gates. Such quantum dot structure is
modeled realistically. Through these simulations we investigate the possibility
of realization of a valley qubit in analogy with a realization of the spin
qubit. We accurately model the potential inside the nanodevice accounting for
proper boundary conditions on the gates and space-dependent materials
permittivity by solving the generalized Poisson's equation. The time-evolution
of the system is supported by realistic self-consistent Poisson-Schr\"odinger
tight-binding calculations. The tight-binding calculations are further
confirmed by simulations within the effective continuum model.
