  Research on spatially inhomogeneous weakly-coupled superconductors has
recently received a boost of interest because of the experimental observation
of a dramatic enhancement of the kinetic inductance with relatively low losses.
Here, we study the kinetic inductance and the quality factor of a
strongly-disordered weakly-coupled superconducting thin film. We employ a
gauge-invariant random-phase approximation capable of describing collective
excitations and other fluctuations. In line with the experimental findings, we
have found that in the range of frequencies of interest, and for sufficiently
low temperatures, an exponential increase of the kinetic inductance with
disorder coexists with a still large quality factor $\sim 10^4$. More
interestingly, on the metallic side of the superconductor-insulator transition,
we have identified a range of frequencies and temperatures $T \sim 0.1T_c$
where quantum coherence effects induce a broad statistical distribution of the
quality factor with an average value that increases with disorder. We expect
these findings to further stimulate experimental research on the design and
optimization of superinductors for a better performance and miniaturization of
quantum devices such as qubit circuits and microwave detectors.
