论文标题
用于无监督学习的量子光谱聚类算法
Quantum spectral clustering algorithm for unsupervised learning
论文作者
论文摘要
聚类是无监督学习中最关键的问题之一，众所周知的$ k $ - 均值聚类算法已证明可以在具有显着加速的量子计算机上实现。但是，许多集群问题无法通过$ k $ - 表示解决，并且引入了一种称为光谱聚类的强大方法来解决这些问题。在这项工作中，我们提出了一种电路设计，以通过将处理器初始化为最大纠缠的状态并将数据信息编码为有效模拟的Hamiltonian，以实现具有实质性加速的量子处理器上的光谱聚类。与已建立的量子$ K $ -MEANS算法相比，我们的方法不需要量子随机访问存储器或量子绝热过程。它依赖于将量子相估计的适当嵌入到Grover的搜索中以获得量子加速。模拟表明，我们的方法有效地解决了聚类问题，并将成为量子$ k $ - 平均无监督学习的重要补充。
Clustering is one of the most crucial problems in unsupervised learning, and the well-known $k$-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering problems cannot be solved by $k$-means, and a powerful method called spectral clustering is introduced to solve these problems. In this work, we propose a circuit design to implement spectral clustering on a quantum processor with a substantial speedup, by initializing the processor into a maximally entangled state and encoding the data information into an efficiently-simulatable Hamiltonian. Compared with the established quantum $k$-means algorithms, our method does not require a quantum random access memory or a quantum adiabatic process. It relies on an appropriate embedding of quantum phase estimation into Grover's search to gain the quantum speedup. Simulations demonstrate that our method is effective in solving clustering problems and will serve as an important supplement to quantum $k$-means for unsupervised learning.
