  We perform numerical simulations of lattice QCD with two flavors of dynamical
overlap quarks, which have exact chiral symmetry on the lattice. While this
fermion discretization is computationally demanding, we demonstrate the
feasibility to simulate reasonably large and fine lattices by a careful choice
of the lattice action and algorithmic improvements. Our production runs are
carried out on a 16^3 \times 32 lattice at a single lattice spacing around 0.12
fm. We explore the sea quark mass region down to m_s/6, where m_s is the
physical strange quark mass, for a good control of the chiral extrapolation in
future calculations of physical observables. We describe in detail our setup
and algorithmic properties of the production simulations and present results
for the static quark potential to fix the lattice scale and the locality of the
overlap operator.
