  Machine learning with hierarchical quantum circuits, usually referred to as
Quantum Convolutional Neural Networks (QCNNs), is a promising prospect for
near-term quantum computing. The QCNN is a circuit model inspired by the
architecture of Convolutional Neural Networks (CNNs). CNNs are successful
because they do not need manual feature design and can learn high-level
features from raw data. Neural Architecture Search (NAS) builds on this success
by learning network architecture and achieves state-of-the-art performance.
However, applying NAS to QCNNs presents unique challenges due to the lack of a
well-defined search space. In this work, we propose a novel framework for
representing QCNN architectures using techniques from NAS, which enables search
space design and architecture search. Using this framework, we generate a
family of popular QCNNs, those resembling reverse binary trees. We then
evaluate this family of models on a music genre classification dataset, GTZAN,
to justify the importance of circuit architecture. Furthermore, we employ a
genetic algorithm to perform Quantum Phase Recognition (QPR) as an example of
architecture search with our representation. This work provides a way to
improve model performance without increasing complexity and to jump around the
cost landscape to avoid barren plateaus. Finally, we implement the framework as
an open-source Python package to enable dynamic QCNN creation and facilitate
QCNN search space design for NAS.
