2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/93012Classically, determining the gradient of a black-box function f:R^p->R requires p+1 evaluations. Using the quantum Fourier transform, two evaluations suffice. This is based on the approximate local periodicity of exp(2*pi*i*f(x)). It is shown that sufficiently precise machine arithmetic results in gradient estimates of any required accuracy.8 pages, no figureQuantum Physicstext