Implementing quantum gates through scattering between a static and a flying qubit

We investigate whether a two-qubit quantum gate can be implemented in a scattering process involving a flying and a static qubit. We focus on a paradigmatic setup made out of a mobile particle and a quantum impurity, whose respective spin degrees of freedom couple to each other during a one-dimensional scattering process. A condition for the occurrence of quantum gates is derived in terms of spin-dependent transmission coefficients. This can be fulfilled through the insertion of an additional narrow potential barrier. Under resonance conditions this procedure enables a gate only for Heisenberg interactions and fails for an XY interaction. We show the existence of parameter regimes for which gates able to establish a maximum amount of entanglement can be implemented. The gates are found to be robust to variations of the optimal parameters.