  This study presents a simulated quantum computing approach for the
investigation into the shell-model energy levels of $^{58}$Ni through the
application of the variational eigensolver (VQE) method in combination with a
problem-specific ansatz. The primary objective is to achieve a fully accurate
low-lying energy spectrum of $^{58}$Ni. The chosen isotope, $^{58}$Ni is
particularly interesting in nuclear physics through its role in astrophysical
reactions while also being a simple but not-trivial nucleus for shell-model
study, it being two particles outside a closed shell. Our ansatz, along with
the VQE method are shown to be able to reproduce exact energy values for the
ground state and first and second excited states. We compare a classical shell
model code, the values obtained by diagonalization of the Hamiltonian after
qubit mapping, and a noiseless simulated ansatz+VQE simulation. The exact
agreement between classical and qubit-mapped diagonalisation shows the
correctness of our method, and the high accuracy of the simulation means that
the ansatz is suitable to allow a full reconstruction of the full nuclear wave
function.
