Understanding the effects of data encoding on quantum-classical convolutional neural networks

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.