  We show how the spin independent scattering of two initially distant qubits,
say, in distinct traps or in remote sites of a lattice, can be used to
implement an entangling quantum gate between them. The scattering takes place
under 1D confinement for which we consider two different scenarios: a 1D
wave-guide and a tight-binding lattice. We consider models with contact-like
interaction between two fermionic or two bosonic particles. A qubit is encoded
in two distinct spins (or other internal) states of each particle. Our scheme
enables the implementation of a gate between two qubits which are initially too
far to interact directly, and provides an alternative to photonic mediators for
the scaling of quantum computers. Fundamentally, an interesting feature is that
"identical particles" (e.g., two atoms of the same species) and the 1D
confinement, are both necessary for the action of the gate. Finally, we discuss
the feasibility of our scheme, the degree of control required to initialize the
wave-packets momenta, and show how the quality of the gate is affected by
momentum distributions and initial distance. In a lattice, the control of
quasi-momenta is naturally provided by few local edge impurities in the lattice
potential.
