  For the quasi-periodic Schr\"{o}dinger operators in the local perturbative
regime where the frequency is Diophantine and the potential is $C^k$
sufficiently small depending on the Diophantine constants, we prove that the
length of the corresponding spectral gap has a polynomial decay upper bound
with respect to its label. This is based on a refined quantitative reducibility
theorem for $C^k$ quasi-periodic ${\rm SL}(2,\mathbb{R})$ cocycles, and also
based on the Moser-P\"{o}schel argument for the related Schr\"{o}dinger
cocycles. As an application, we are able to show the homogeneity of the
spectrum.
