  We study the variation in the Land$\acute{\text{e}}$ g-factor of electron
spins induced by both anisotropic gate potentials and magnetic fields in InAs
quantum dots for possible implementation towards solid state quantum computing.
In this paper, we present analytical expressions and numerical simulations of
the variation in the Land$\acute{\text{e}}$ g-factor for both isotropic and
anisotropic quantum dots. Using both analytical techniques and numerical
simulations, we show that the Rashba spin-orbit coupling has a major
contribution in the variation of the g-factor with electric fields before the
regime, where level crossing or anticrossing occurs. In particular, the
electric field tunability is shown to cover a wide range of g-factor through
strong Rashba spin-orbit interaction. Another major result of this paper is
that the anisotropic gate potential gives quenching effect in the orbital
angular momentum that reduces the variation in the E-field and B-field
tunability of the g-factor if the area of the symmetric and asymmetric quantum
dots is held constant. We identify level crossings and anticrossings of the
electron states in the variation of the Land$\acute{\text{e}}$ g-factor. We
model the wavefunctions of electron spins and estimate the size of the
anticrossing for the spin states $|0,-1,+1/2>$ and $|0,0,-1/2>$ corresponding
to a quantum dot that has been recently studied experimentally (Phys. Rev.
Lett. \textbf{104}, 246801 (2010)).
