  An active area of investigation in the search for quantum advantage is
Quantum Machine Learning. Quantum Machine Learning, and Parameterized Quantum
Circuits in a hybrid quantum-classical setup in particular, could bring
advancements in accuracy by utilizing the high dimensionality of the Hilbert
space as feature space. But is the ability of a quantum circuit to uniformly
address the Hilbert space a good indicator of classification accuracy? In our
work, we use methods and quantifications from prior art to perform a numerical
study in order to evaluate the level of correlation. We find a strong
correlation between the ability of the circuit to uniformly address the Hilbert
space and the achieved classification accuracy for circuits that entail a
single embedding layer followed by 1 or 2 circuit designs. This is based on our
study encompassing 19 circuits in both 1 and 2 layer configuration, evaluated
on 9 datasets of increasing difficulty. Future work will evaluate if this holds
for different circuit designs.
