  It has been a big challenge for lattice QCD to simulate dynamical quarks near
the chiral limit. Theoretically, it is well-known that the naive chiral
symmetry cannot be realized on the lattice (the Nielsen-Ninomiya theorem). Also
practically, the computational cost rapidly grows as the quark mass is reduced.
The JLQCD collaboration started a project to perform simulations with exact but
modified chiral symmetry using the the overlap-Dirac operator and the topology
conserving action. The latter is helpful to reduce the numerical cost of the
dynamical quarks. Our simulation of two-flavor QCD has been successful to
reduce the sea quark mass down to a few MeV.
