Quantum Topological Data Encoding

• URL: http://arxiv.org/abs/2607.13847v1
• Date: Wed, 15 Jul 2026 13:53:48 GMT
• Title: Quantum Topological Data Encoding
• Abstract summary: We introduce emphquantum topological data encoding (QTDE), a general framework for encoding topological information into quantum states.<n>We test the proposed method on clique-complexes classification tasks, and provide preliminary comparisons of classical topological descriptors.<n>We indicate several areas of application where the framework can be used to provide a more efficient reliable data representation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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