  In this paper we show how to measure in the setting of digital quantum
simulations the reflection and transmission amplitudes of the one-dimensional
scattering of a particle with a short-ranged potential. The main feature of the
protocol is the coupling between the particle and an ancillary spin-1/2 degree
of freedom. This allows us to reconstruct tomographically the scattering
amplitudes, which are in general complex numbers, from the readout of one
qubit. Applications of our results are discussed.
