  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 CZ gate (universal for quantum computation)
between them. This occurs quasi-deterministically in a single scattering event,
hence with no need for any post-selection 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.
