论文标题
通过实施量子拓扑分析了解编码数据的映射
Understanding the Mapping of Encode Data Through An Implementation of Quantum Topological Analysis
论文作者
论文摘要
量子机学习的潜在优势源于使用量子电路将经典数据编码为高维复杂的希尔伯特空间的能力。最近的研究表明，在表示经典数据时，并非所有编码方法都是相同的，因为某些参数化电路结构比其他参数化的电路结构更具表现力。在这项研究中，我们显示编码技术的差异可以通过研究复杂的希尔伯特空间中嵌入的数据的拓扑来可视化。可视化技术是一种基于混合量子的拓扑分析，它使用边界操作员的简单对角线化来计算持续的betti数字和持久的同源图。为了增加NISQ框架内Betti数字的计算，我们建议一种简单的混合算法。通过一个综合数据集的照明示例以及角度编码，振幅编码和IQP编码的方法，我们通过编码方法以及原始数据揭示了拓扑差异。因此，我们的结果表明，需要在不同的量子机学习模型中仔细考虑编码方法，因为它可以强烈影响下游分析（例如聚类或分类）。
A potential advantage of quantum machine learning stems from the ability of encoding classical data into high dimensional complex Hilbert space using quantum circuits. Recent studies exhibit that not all encoding methods are the same when representing classical data since certain parameterized circuit structures are more expressive than the others. In this study, we show the difference in encoding techniques can be visualized by investigating the topology of the data embedded in complex Hilbert space. The technique for visualization is a hybrid quantum based topological analysis which uses simple diagonalization of the boundary operators to compute the persistent Betti numbers and the persistent homology graph. To augment the computation of Betti numbers within a NISQ framework, we suggest a simple hybrid algorithm. Through a illuminating example of a synthetic data set and the methods of angle encoding, amplitude encoding, and IQP encoding, we reveal topological differences with the encoding methods, as well as the original data. Consequently, our results suggest the encoding method needs to be considered carefully within different quantum machine learning models since it can strongly affect downstream analysis like clustering or classification.
