  We consider an inhomogeneous anisotropic gap superconductor in the vicinity
of the quantum critical point, where the transition temperature is suppressed
to zero by disorder. Starting with the BCS Hamiltonian, we derive the
Ginzburg-Landau action for the superconducting order parameter. It is shown
that the critical theory corresponds to the marginal case in two dimensions and
is formally equivalent to the theory of an antiferromagnetic quantum critical
point, which is a quantum critical theory with the dynamic critical exponent,
z=2. This allows us to use a parquet method to calculate the non-perturbative
effect of quantum superconducting fluctuations on thermodynamic properties. We
derive a general expression for the fluctuation magnetic susceptibility, which
exhibits a crossover from the logarithmic dependence, $\chi ~ ln(dn)$, valid
beyond the Ginzburg region to $\chi ~ ln^{1/5}(dn)$ valid in the immediate
vicinity of the transition (where $dn$ is the deviation from the critical
disorder concentration). We suggest that the obtained non-perturbative results
describe the low-temperature critical behavior of a variety of diverse
superconducting systems, which include overdoped high-temperature cuprates,
disordered p-wave superconductors, and conventional superconducting films with
magnetic impurities.
