  The pion-mass-dependent nucleon-nucleon ($NN$) potentials in term of one-pion
exchange and contact terms are obtained from the latest lattice QCD simulations
of two-nucleon system, which employ the forms of leading order (LO) $NN$
potential from the chiral effective field theory and thus are named as the LO
chiral potential in this work. We extract the coefficients of contact terms and
cut-off momenta in these potentials, for the first time, by fitting the phase
shifts of $^1S_0$ and $^3S_1$ channels generated by the results of HALQCD
collaboration with various pion masses from $468.6$ MeV to $1170.9$ MeV. The
low-energy constants in the $^1S_0$ and $^3S_1$ channels become weaker and
approach each other for larger pion masses. These LO chiral potentials are
applied to symmetric nuclear and pure neutron matter within the
Brueckner-Hartree-Fock method. At this moment, however, we do not have yet the
information of the $P$-wave $NN$ interaction to be provided by the lattice QCD
simulations for full description of nuclear matter. Our results will enhance
the development of nuclear structure and nuclear matter by controlling the
contribution of the pionic effect and illuminate the role of chiral symmetry of
the strong interaction in complex system.
