  In this thesis we expand upon the results that led to the paper of Lee et
al., arXiv:2105.01114 (2021). In particular, we give more details on the
oracular formulation of variational quantum algorithms, and the relationship
between properties of Ans\"atze and the strength of their corresponding
oracles. Furthermore, having identified the importance of noncommutativity in
parameterized quantum circuits (PQCs) as likely being crucial to achieving a
quantum advantage, we compare this notion to similar properties in classical
neural networks such as nonlinearity, based on the perspective of the recent
moniker for PQCs as quantum neural networks. While this thesis includes much of
the figures and content from the aforementioned paper, it should be considered
mainly as a self-contained collection of supplementary materials.
