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In this review, we discuss recent developments concerning efficientcalculations of multi-loop multi-leg scattering amplitudes. Inspired by theremarkable properties of the Loop-Tree Duality (LTD), we explain how toreconstruct an integrand level representation of scattering amplitudes whichonly contains physical singularities. These so-called causal representationscan be derived from connected binary partitions of Feynman diagrams, properlyentangled according to specific rules. We will focus on the detection of fluxorientations which are compatible with causality, describing the implementationof a quantum algorithm to identify such configurations.

Geometry and causal flux in multi-loop Feynman diagrams