  We explain why quantum adiabatic evolution and simulated annealing perform
similarly in certain examples of searching for the minimum of a cost function
of n bits. In these examples each bit is treated symmetrically so the cost
function depends only on the Hamming weight of the n bits. We also give two
examples, closely related to these, where the similarity breaks down in that
the quantum adiabatic algorithm succeeds in polynomial time whereas simulated
annealing requires exponential time.
