Top-quark physics at the LHC offers two complementary test beds for quantum computing. The first is quantum information in top-quark pairs: since the top quark decays before hadronisation, a tt¯ pair behaves as a two-qubit system whose spin density matrix can be measured. This is a quantum-native problem with a known ground truth. The thesis will consist of establishing a full tomography pipeline with the ATLAS Run 3 data at 13.6 TeV, using quantum circuits, optimisation methods and a quantum parton shower to validate and study the measurements. The second aspect is linked to four-top production, a rare signal with challenging backgrounds, small training samples and a combinatorial many-jet final state. The project will test quantum optimisation (QUBO-based jet-to-parton assignment) and quantum classifiers for signal discrimination against the best classical methods, to find out where quantum approaches bring a real gain in accuracy, data efficiency or scaling.