  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\"{a}tze that take into account the
symmetry properties of the problem and use clever initialization 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.
