  We introduce new techniques that can preserve unitarity of the system
including ghost particles. Negative norms of the particles can be involved in
zero-norm states by constraints of the physical space. These are useful to
apply the higher-derivative propagator for quantum gravity to suppress
divergences of vacuum energy and graviton mass correction. The quantum effects
are mainly depending on the ghost mass scale. As the scale can be chosen in any
order, the observed cosmological constant is realized. Further, applying ghost
partners for the standard model particles, quantum gravity with matter fields
becomes renormalizable with power counting arguments.
