Topological data analysis offers a robust way to extract useful information from noisy, unstructured data by identifying its underlying structure. Recently, an efficient quantum algorithm was proposed [Nat. Commun. 7, 10138 (2016) [CrossRef] ] for calculating Betti numbers of data points—topological features that count the number of topological holes of various dimensions in a scatterplot. Here, we implement a proof-of-principle demonstration of this quantum algorithm by employing a six-photon quantum processor to successfully analyze the topological features of Betti numbers of a network including three data points, providing new insights into data analysis in the era of quantum computing.

中文翻译：

---

在量子处理器上演示拓扑数据分析

拓扑数据分析提供了一种可靠的方法，可通过识别其底层结构从嘈杂的非结构化数据中提取有用的信息。最近，提出了一种有效的量子算法。公社 7，10138（2016）[交叉引用] ]用于计算数据的贝蒂数点拓扑功能，在计数的散点图各种尺寸的拓扑的孔的数量。在这里，我们通过使用六光子量子处理器成功地分析包括三个数据点的网络的贝蒂数的拓扑特征，对该量子算法进行了原理证明，为当今时代的数据分析提供了新的见解。量子计算。