  Motivated by graphene-based quantum computer we examine the time-dependence
of the position-momentum and position-velocity uncertainties in the monolayer
gapped graphene. The effect of the energy gap to the uncertainties is shown to
appear via the Compton-like wavelength $\lambda_c$. The uncertainties in the
graphene are mainly contributed by two phenomena, spreading and zitterbewegung.
While the former determines the uncertainties in the long-range of time, the
latter gives the highly oscillation to the uncertainties in the short-range of
time. The uncertainties in the graphene are compared with the corresponding
values for the usual free Hamiltonian $\hat{H}_{free} = (p_1^2 + p_2^2) / 2 M$.
It is shown that the uncertainties can be under control within the quantum
mechanical law if one can choose the gap parameter $\lambda_c$ freely.
