Quantum geometric machine learning
- Publication Type:
- Thesis
- Issue Date:
- 2024
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The use of geometric and symmetry techniques in quantum and classical information processing has a long tradition across the physical sciences as a means of theoretical discovery and applied problem solving. In the modern era, the emergent combination of such geometric and symmetry-based methods with quantum machine learning (QML) has provided a rich opportunity to contribute to solving a number of persistent challenges in fields such as QML parametrisation, quantum control, quantum unitary synthesis and quantum proof generation. In this thesis, we combine state-of-the-art machine learning methods with techniques from differential geometry and topology to address these challenges. We present a large-scale simulated dataset of open quantum systems to facilitate the development of quantum machine learning as a field. We demonstrate the use of deep learning greybox machine learning techniques for estimating approximate time-optimal unitary sequences as geodesics on subRiemannian symmetric space manifolds. Finally, we present novel techniques utilising Cartan decompositions and variational methods for analytically solving quantum control problems for certain classes of Riemannian symmetric space.
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