Quantum machine learning has received significant interest in recent years, with theoretical studies showing that quantum variants of classical machine learning algorithms can provide good generalization from small training data sizes. However, there are notably no strong theoretical insights about what makes a quantum circuit design better than another, and comparative studies between quantum equivalents have not been done for every type of classical layers or techniques crucial for classical machine learning. Particularly, the pooling layer within convolutional neural networks is a fundamental operation left to explore. Pooling mechanisms significantly improve the performance of classical machine learning algorithms by playing a key role in reducing input dimensionality and extracting clean features from the input data.

In this thesis, an in-depth study of pooling techniques in hybrid quantum-classical convolutional neural networks (QCCNNs) for classifying 2D medical images is performed. The performance of three different quantum and hybrid pooling techniques is studied: mid-circuit measurements, ancilla qubits with controlled gates, and qubit selection with classical postprocessing.