Quantum transport is the study of how electrons propagate through conductors while retaining their wave-like coherence. It explains phenomena related to the wave nature of electrons such as conductance quantization, Aharonov-Bohm effect, weak localization, universal conductance fluctuations, and many others. Computational quantum transport is almost as old as the associated theory, however the existing approaches struggle with system sizes large enough to describe relevant experiments, especially in three dimensions. In this PhD project, we will build on a recent breakthrough in quantum-inspired approaches (https://scipost.org/SciPostPhys.18.3.104) to develop quantum transport methods that scale well beyond existing ones. Our working hypothesis is that the scattering wave function at the core of quantum transport theory can be strongly compressed using a tensor network representation. This approach is analogous to that taken for the quantum many-body problem in the density matrix renormalization group framework. In a second stage, we will apply this method in 2D to various difficult problems related to graphene-based electronic interferometers and in 3D to topological materials. This project requires good mathematical skills and experience with scientific programming. The work will involve theoretical as well as numeric aspects.