  We present preliminary results for the contributions to the neutron EDM
arising from the QCD $\theta$-term, the Weinberg three-gluon and the quark
chromo-EDM operators from our ongoing lattice calculations using clover valence
quarks on the MILC HISQ lattices. We use the gradient-flow technique to smooth
the lattices and renormalize the gluonic operators, and use the Schwinger
source method to incorporate the quark chromo-EDM interactions in the quark
propagator. For the QCD $\theta$-term and the Weinberg three-gluon operator, we
report results in the gradient-flow scheme from 8 ensembles at four lattice
spacings and three pion masses, including 2 physical pion mass ensembles. For
the quark chromo-EDM, unrenormalized results are presented at two lattice
spacings, $a=0.12$ and $0.09$ fm, and two pion masses, $M_\pi = 310$ MeV and
$220$ MeV.
