We show that a flying particle, such as an electron or a photon, scattering along a one-dimensional waveguide from a pair of static spin-1/2 centers, such as quantum dots, can implement a controlled-z gate (universal for quantum computation) between them. This occurs quasideterministically in a single scattering event, with no need for any postselection or iteration and without demanding the flying particle to bear any internal spin. We show that an easily matched hard-wall boundary condition along with the elastic nature of the process are key to such performances.