  The anti-de Sitter/conformal field theory correspondence (AdS/CFT) has been
used to determine a lower bound on the ratio of shear viscosity
$\left(\eta\right)$ to entropy density $(s)$ for strongly-coupled field
theories with a gravity dual. The conjectured universal lower bound, given as
$\eta/s\geq\hbar/4\pi k_B$, is a measure of interaction strength in a quantum
fluid where equality indicates a perfect quantum fluid. In this paper we study
$\eta/s$ in a Fermi gas in the unitary limit. We show that in addition to a
local minimum for $\eta/s$ at $T\approx 2T_c$ which obeys the lower bound, a
more interesting result exists in the violation of the $\eta/s$ lower bound due
to the superfluid fluctuations above $T_c$. To conclude, we examine the
viscoelastic properties of the unitary Fermi gas. Previous work brought to
light the connection between violation of the $\eta/s$ bound and a viscoelastic
response in the context of holographic solids. We ultimately find that, in
addition to holographic solids, all Fermi liquids with a viscoelastic response
produced by superfluid fluctuations can violate the universal $\eta/s$ lower
bound.
