2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229112In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be a sparse matrix with all entries equal to 0 or 1, i.e., the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any desired quantum computation encoded entirely in some underlying graph. The main idea of the construction is to implement quantum gates by scattering processes.9 pagesQuantum Physicstext