  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 work,
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 four different quantum and hybrid pooling
techniques is studied: mid-circuit measurements, ancilla qubits with controlled
gates, modular quantum pooling blocks and qubit selection with classical
postprocessing. We find similar or better performance in comparison to an
equivalent classical model and QCCNN without pooling and conclude that it is
promising to study architectural choices in QCCNNs in more depth for future
applications.
