  We derive the equation of state of nuclear matter including vacuum
polarization effects arising from the nucleons and the sigma mesons in the
quark-meson coupling model which incorporates explicitly quark degrees of
freedom with quark coupled to the scalar and vector mesons. This leads to a
softer equation of state for nuclear matter giving a lower value of
incompressibility than would be reached without quantum effects. The {\it
in-medium} nucleon and sigma meson masses are also calculated in a
self-consistent manner.
