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Quantum Gates Between Flying Qubits via Spin-Independent Scattering

We show how the spin independent scattering between two identical flying qubits can be used to implement an entangling quantum gate between them. We consider one dimensional models with a delta interaction in which the qubits undergoing the collision are distinctly labeled by their opposite momenta. The logical states of the qubit may either be two distinct spin (or other internal) states of a fermion or a boson or two distinct momenta magnitudes of a spinless boson. Our scheme could be added to linear optics-like quantum information processing to enhance its efficiency, and can also aid the scaling of quantum computers based on static qubits without resorting to photons. Three distinct ingredients -- the quantum indistinguishability of the qubits, their interaction, and their dimensional confinement, come together in a natural way to enable the quantum gate.