  We elaborate that $s$-wave and $d$-wave superconductors described by mean
field theories possess a nontrivial quantum geometry. From the overlap of two
quasihole states at slightly different momenta, one can define a quantum metric
that measures the distance in the curved momentum space. The
momentum-integration of the quantum metric represents an average distance that
we call the fidelity number, which may be further expressed as a fidelity
marker defined locally on every lattice site. For $s$-wave superconductors, we
unveil that the quantum metric generally influences the electromagnetic
responses at finite wave length, such as the infrared absorption and
paramagnetic current. In addition, the dielectric response is directly
proportional to the fidelity number, which is found to be determined by the
coherence length and suppressed by disorder. For $d$-wave superconductors, we
demonstrate the singular behavior of the quantum metric near the nodal points,
and a metric-curvature correspondence between the azimuthal quantum metric and
the non-Abelian Berry connection that integrates to a topological charge of the
nodal points.
