2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/89964We 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.16pp., 10 EPS figures, using BoxedEPS macros and LaTeX. Email correspondence to E. Farhi <farhi@mit.edu>Quantum Physicstext