The Lipkin and Agassi models are simplified nuclear models that provide natural test beds for quantum simulation methods. Prior work has investigated the suitability of the variational quantum eigensolver (VQE) to find the ground state of these models. There is a growing awareness that if VQE is to prove viable, we will need problem inspired ans & auml;tze that take into account the symmetry properties of the problem and use clever initialisation strategies. Here, by focusing on the Lipkin and Agassi models, we investigate how to do this in the context of nuclear physics ground state problems. We further use our observations to discus the potential of new classical, but quantum-inspired, approaches to learning ground states in nuclear problems.