论文标题
量子使用矩阵产品状态启发了K-均值算法
Quantum inspired K-means algorithm using matrix product states
论文作者
论文摘要
在研究一维相互作用的量子多体系统时，矩阵乘积状态已成为首选的算法，该系统证明能够探索指数级的大量子希尔伯特空间中最相关的部分并找到准确的解决方案。在这里，我们提出了一种量子启发的K-均值聚类算法，该算法首先将经典数据映射到表示为矩阵乘积状态状态的量子状态，然后使用扩大空间中的变异矩阵量态方法最小化损耗函数。我们通过将其应用于几个常用的机器学习数据集的性能来证明该算法的性能，并表明该算法可以达到更高的预测准确性，并且与经典的K-Means算法相比，该算法不太可能将其捕获到本地最小值中。
Matrix product state has become the algorithm of choice when studying one-dimensional interacting quantum many-body systems, which demonstrates to be able to explore the most relevant portion of the exponentially large quantum Hilbert space and find accurate solutions. Here we propose a quantum inspired K-means clustering algorithm which first maps the classical data into quantum states represented as matrix product states, and then minimize the loss function using the variational matrix product states method in the enlarged space. We demonstrate the performance of this algorithm by applying it to several commonly used machine learning datasets and show that this algorithm could reach higher prediction accuracies and that it is less likely to be trapped in local minima compared to the classical K-means algorithm.
