One of the main advantages of the Loop-Tree Duality representation of scattering amplitudes is that it makes the origin of infrared and threshold singularities particularly transparent. This talk reviews recent progress in describing how singularities emerge and cancel at the level of scattering and vacuum amplitudes, discusses a novel strategy to efficiently construct finite integrals, and presents a complementary perspective based on encoding the underlying causal and singular structure in terms of qubits and quantum circuits.