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

TL;DR

This paper introduces approximately equivariant quantum convolutional neural networks tailored for $p4m$ symmetries in images, demonstrating improved generalization in image classification tasks by leveraging dataset symmetries.

Contribution

It proposes a novel equivariant quantum neural network architecture specifically designed for $p4m$ symmetries, enhancing model generalization and performance in symmetry-aware image classification.

Findings

Equivariant QNNs outperform non-equivariant models in symmetry-based tasks.

The model effectively captures $p4m$ symmetries including reflections and rotations.

Experimental results show improved generalization in phase detection and MNIST classification.

Abstract

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.