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

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.

7 pages, 6 figures, To be published as part of the IEEE Quantum Week 2023 Proceedings

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• Exploiting symmetry in variational quantum machine learning
• Group-Invariant Quantum Machine Learning
• Lorentz Group Equivariant Neural Network for Particle Physics
• Quantum phase detection generalisation from marginal quantum neural network models
• Reflection Equivariant Quantum Neural Networks for Enhanced Image Classification
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Cited by in corpus (6)

• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• On the universality of $S_n$-equivariant $k$-body gates
• The role of data embedding in equivariant quantum convolutional neural networks
• Symmetry-invariant quantum machine learning force fields
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ Equivariant Quantum Neural Networks: Benchmarking against Classical Neural Networks
• Permutation-equivariant quantum convolutional neural networks