  Charge transport is a revealing probe of the quantum properties of materials.
Strong interactions can blur charge carriers resulting in a poorly understood
"quantum soup". Here we study the conductivity of the Fermi-Hubbard model, a
testing ground for strong interaction physics, in a clean quantum system -
ultracold $^6$Li in a 2D optical lattice. We determine the charge diffusion
constant in our system by measuring the relaxation of an imposed density
modulation and modeling its decay hydrodynamically. The diffusion constant is
converted to a resistivity, which exhibits a linear temperature dependence and
exceeds the Mott-Ioffe-Regel limit, two characteristic signatures of a bad
metal. The techniques we develop here may be applied to measurements of other
transport quantities, including the optical conductivity and thermopower.
