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Quantum Neural Networks (QNNs) are suggested as one of the quantum algorithmswhich can be efficiently simulated with a low depth on near-term quantumhardware in the presence of noises. However, their performance highly relies onchoosing the most suitable architecture of Variational Quantum Algorithms(VQAs), and the problem-agnostic models often suffer issues regardingtrainability and generalization power. As a solution, the most recent worksexplore Geometric Quantum Machine Learning (GQML) using QNNs equivariant withrespect to the underlying symmetry of the dataset. GQML adds an inductive biasto the model by incorporating the prior knowledge on the given dataset andleads to enhancing the optimization performance while constraining the searchspace. This work proposes equivariant Quantum Convolutional Neural Networks(EquivQCNNs) for image classification under planar $p4m$ symmetry, includingreflectional and $90^\circ$ rotational symmetry. We present the results testedin different use cases, such as phase detection of the 2D Ising model andclassification of the extended MNIST dataset, and compare them with thoseobtained with the non-equivariant model, proving that the equivariance fostersbetter generalization of the model.

Approximately Equivariant Quantum Neural Network for $p4m$ Group Symmetries in Images