  We design an adiabatic quantum algorithm for the counting problem, i.e.,
approximating the proportion, $\alpha$, of the marked items in a given
database. As the quantum system undergoes a designed cyclic adiabatic
evolution, it acquires a Berry phase $2\pi\alpha$. By estimating the Berry
phase, we can approximate $\alpha$, and solve the problem. For an error bound
$\epsilon$, the algorithm can solve the problem with cost of order
$(\frac{1}{\epsilon})^{3/2}$, which is not as good as the optimal algorithm in
the quantum circuit model, but better than the classical random algorithm.
Moreover, since the Berry phase is a purely geometric feature, the result may
be robust to decoherence and resilient to certain noise.
