  We report on the progress of our study on the color-electric correlation
functions under gradient flow on the lattice. This calculation is the first
step of our long-term project to estimate a series of important transport
coefficients, of which the heavy quark momentum diffusion coefficient is our
first attempt, as it can be extracted from a color-electric correlation
function that has been calculated non-perturbatively using noise reduction
technique in the quenched approximation [1]. By comparing the flowed
correlation function with those obtained by other signal-improving techniques,
for instance the multi-level algorithm used in [1], one can gain insight into
the applicability of the gradient flow and the renormalization of the
correlation functions.
  We start with quenched, isotropic lattices. Currently we have finished
measuring the color-electric correlation functions on 4 different lattices with
$\beta$-values corresponding to a temperature of $T\approx 1.5T_c$. We perform
a continuum extrapolation on the flowed correlators at fixed physical flow
times followed by an extrapolation of the continuum estimate back to zero flow
time. The next step is to extend the study to different temperatures and to
extend the study to dynamical QCD.
