量子持久同调
Quantum Persistent Homology
摘要：
持久同源性是一个强大的数学工具，它总结了有关数据形状的有用信息，允许人们在调整分辨率时检测持久拓扑特征。然而，这种拓扑特征的计算通常是一项相当艰巨的任务，需要对底层数据进行二次采样。为了解决这个问题，我们开发了一个有效的量子计算的持久贝蒂数，跟踪不同尺度的数据的拓扑特征。我们的方法采用了一个持久的狄拉克算子，其平方产生持久的组合拉普拉斯算子，并反过来捕获数据的持久性特征的潜在持久贝蒂数。我们还测试我们的算法上的点云数据。
英文摘要：
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such topological features is often a rather formidable task necessitating the subsampling the underlying data. To remedy this, we develop an efficient quantum computation of persistent Betti numbers, which track topological features of data across different scales. Our approach employs a persistent Dirac operator whose square yields the persistent combinatorial Laplacian, and in turn the underlying persistent Betti numbers which capture the persistent features of data. We also test our algorithm on point cloud data.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
