Approximately Equivariant Quantum Neural Network for $p4m$ Group
  Symmetries in Images
Su Yeon Chang Michele Grossi Bertrand Le Saux Sofia Vallecorsa
Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithms
which can be efficiently simulated with a low depth on near-term quantum
hardware in the presence of noises. However, their performance highly relies on
choosing the most suitable architecture of Variational Quantum Algorithms
(VQAs), and the problem-agnostic models often suffer issues regarding
trainability and generalization power. As a solution, the most recent works
explore Geometric Quantum Machine Learning (GQML) using QNNs equivariant with
respect to the underlying symmetry of the dataset. GQML adds an inductive bias
to the model by incorporating the prior knowledge on the given dataset and
leads to enhancing the optimization performance while constraining the search
space. This work proposes equivariant Quantum Convolutional Neural Networks
(EquivQCNNs) for image classification under planar $p4m$ symmetry, including
reflectional and $90^\circ$ rotational symmetry. We present the results tested
in different use cases, such as phase detection of the 2D Ising model and
classification of the extended MNIST dataset, and compare them with those
obtained with the non-equivariant model, proving that the equivariance fosters
better generalization of the model.