  Quantum machine learning was recently applied to various applications and
leads to results that are comparable or, in certain instances, superior to
classical methods, in particular when few training data is available. These
results warrant a more in-depth examination of when and why improvements can be
observed. A key component of quantum-enhanced methods is the data encoding
strategy used to embed the classical data into quantum states. However, a clear
consensus on the selection of a fitting encoding strategy given a specific
use-case has not yet been reached. This work investigates how the data encoding
impacts the performance of a quantum-classical convolutional neural network
(QCCNN) on two medical imaging datasets. In the pursuit of understanding why
one encoding method outperforms another, two directions are explored. Potential
correlations between the performance of the quantum-classical architecture and
various quantum metrics are first examined. Next, the Fourier series
decomposition of the quantum circuits is analyzed, as variational quantum
circuits generate Fourier-type sums. We find that while quantum metrics offer
limited insights into this problem, the Fourier coefficients analysis appears
to provide better clues to understand the effects of data encoding on QCCNNs.
