Reflection Equivariant Quantum Neural Networks for Enhanced Image Classification

Abstract

Machine learning is among the most widely anticipated use cases for near-term quantum computers, however there remain significant theoretical and implementation challenges impeding its scale up. In particular, there is an emerging body of work which suggests that generic, data agnostic quantum machine learning (QML) architectures may suffer from severe trainability issues, with the gradient of typical variational parameters vanishing exponentially in the number of qubits. Additionally, the high expressibility of QML models can lead to overfitting on training data and poor generalisation performance. A promising strategy to combat both of these difficulties is to construct models which explicitly respect the symmetries inherent in their data, so-called geometric quantum machine learning (GQML). In this work, we utilise the techniques of GQML for the task of image classification, building new QML models which are equivariant with respect to reflections of the images. We find that these networks are capable of consistently and significantly outperforming generic ansatze on complicated real-world image datasets, bringing high-resolution image classification via quantum computers closer to reality. Our work highlights a potential pathway for the future development and implementation of powerful QML models which directly exploit the symmetries of data.

7 pages, 6 figures

References in corpus (11)

• Exploiting symmetry in variational quantum machine learning
• Supervised quantum machine learning models are kernel methods
• Group-Invariant Quantum Machine Learning
• Hybrid Quantum-Classical Generative Adversarial Network for High Resolution Image Generation
• Towards quantum enhanced adversarial robustness in machine learning
• Benchmarking Adversarially Robust Quantum Machine Learning at Scale
• Building spatial symmetries into parameterized quantum circuits for faster training
• Representation Theory for Geometric Quantum Machine Learning
• Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data
• Boosted Ensembles of Qubit and Continuous Variable Quantum Support Vector Machines for B Meson Flavour Tagging
• GASP -- A Genetic Algorithm for State Preparation

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