Speakers
Description
Many datasets encountered across a wide range of domains possess rich geometric and topological structure that is difficult to capture using conventional vector-based representations. Quantum machine learning offers the possibility of processing high-dimensional data in Hilbert spaces, but its practical success depends critically on how classical data is encoded into quantum states. We introduce quantum topological data encoding (QTDE), a general framework for encoding topological information into quantum states via topology-driven quantum evolution. Our method generalises an existing topology-driven quantum encoding framework to higher-dimensional data. We test the proposed method on classification tasks, and provide preliminary evidence that the proposed methodology may be capable of surpassing classical data representation capabilities. The proposed quantum representations yield consistently superior results compared to a method based on direct comparison of the Laplacian matrices that classically describe the topological data. We indicate several areas of application where the framework can used to provide a more efficient and reliable data representation.
| Topic | Encoding and processing of data in quantum systems |
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| Additional Topic | Theoretical foundations of quantum learning |