  We study the effects of the quantum geometric tensor, i.e., the Berry
curvature and the Fubini-Study metric, on the steady state of
driven-dissipative bosonic lattices. We show that the quantum-Hall-type
response of the steady-state wave function in the presence of an external
potential gradient depends on all the components of the quantum geometric
tensor. Looking at this steady-state Hall response, one can map out the full
quantum geometric tensor of a sufficiently flat band in momentum space using a
driving field localized in momentum space. We use the two-dimensional Lieb
lattice as an example and numerically demonstrate how to measure the quantum
geometric tensor.
