  Key properties of physical systems can be described by the eigenvalues of
matrices that represent the system. Computational algorithms that determine the
eigenvalues of these matrices exist, but they generally suffer from a loss of
performance as the matrix grows in size. This process can be expanded to
quantum computation to find the eigenvalues with better performance than the
classical algorithms. One application of such an eigenvalue solver is to
determine energy levels of a molecule given a matrix representation of its
Hamiltonian using the variational principle. Using a variational quantum
eigensolver, we determine the ground state energies of different molecules. We
focus on the choice of optimization strategy for a Qiskit simulator on low-end
hardware. The benefits of several different optimizers were weighed in terms of
accuracy in comparison to an analytic classical solution as well as code
efficiency.
