  We consider random conductance models with long range jumps on $\Z^d$, where
the one-step transition probability from $x$ to $y$ is proportional to
$w_{x,y}|x-y|^{-d-\alpha}$ with $\alpha\in (0,2)$. Assume that
$\{w_{x,y}\}_{(x,y)\in E}$ are independent, identically distributed and
uniformly bounded non-negative random variables with $\Ee w_{x,y}=1$, where $E$
is the set of all unordered pairs on $\Z^d$. We obtain a quantitative version
of stochastic homogenization for these random walks, with explicit polynomial
rates up to logarithmic corrections.
