Quantum Topological Data Encoding
Abstract
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 \emph{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 clique-complexes classification tasks, and provide preliminary evidence that topology-driven quantum representations can capture discriminative information beyond that available through direct comparisons of classical topological descriptors. The proposed quantum representations consistently outperform a baseline based on direct comparisons of the combinatorial Laplacians describing the underlying topological structure. We indicate several areas of application where the framework can be used to provide a more efficient and reliable data representation.
Authors 4
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Royal Holloway University of London
Affiliation as printed
Royal Holloway University of London , Department of Computer Science , UK
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Affiliation as printed
Leiden Institute of Advanced Computer Science (LIACS) , Leiden University , Leiden , The Netherlands
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Singapore University of Technology and Design · Singapore Institute of Technology
Affiliation as printed
Science, Mathematics and Technology Cluster , Singapore University of Technology and Design , Singapore
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National University of Singapore · Centre for Quantum Technologies
Affiliation as printed
Centre for Quantum Technologies , National University of Singapore , Singapore