  We study correlation functions of the energy-momentum tensor (EMT) in
$(2+1)$-flavor full QCD to evaluate QGP viscosities. We adopt nonperturbatively
improved Wilson fermion and Iwasaki gauge action. Our degenerate $u$, $d$ quark
mass is rather heavy with $m_{\pi}/m_{\rho}\simeq0.63$, while the $s$ quark
mass is set to approximately its physical value. Performing simulations on
lattices with $N_t=16$ to 6 at a fine lattice spacing of $a=0.07$ fm, the
temperature range of $T\simeq174$--$464$ MeV is covered using the fixed-scale
approach. We attempt to compute viscosities by three steps: (1) calculate two
point correlation functions of non-perturbatively renormalized EMT applying the
gradient flow method, (2) derive the spectral function from correlation
function, and (3) extract viscosities from the spectral function applying the
Kubo formula. We report on the status of the project and present preliminary
results for the shear viscosity in the high temperature phase.
