用拓扑驱动的量子演化编码数据,提升高维结构信息捕捉能力
Quantum Topological Data Encoding

- 基于拓扑结构引导量子态演化,实现高维数据编码
- 在团复形分类任务中优于基于组合拉普拉斯的基线方法
- 适合处理含复杂几何拓扑结构的数据分析场景
跨多个领域的许多数据集具有丰富的几何与拓扑结构,传统向量表示难以捕捉。量子机器学习可在希尔伯特空间处理高维数据,但其实际效果关键取决于经典数据如何编码为量子态。我们提出量子拓扑数据编码(QTDE),通过拓扑驱动的量子演化将拓扑信息编码至量子态,推广了现有拓扑驱动编码框架至高维数据。在团复形分类任务中测试表明,拓扑驱动的量子表示能捕捉超出直接比较经典拓扑描述子的信息。所提量子表示持续优于基于组合拉普拉斯对比的基线方法。该框架在多个应用场景中可提供更高效可靠的特征表示。
原文摘要 · Abstract (English)
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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