Machine learning algorithms perform well on identifying patterns in many different datasets due to their versatility. However, as one increases the size of the dataset, the computation time for training and using these statistical models grows quickly. Quantum computing offers a new paradigm which may have the ability to overcome these computational difficulties. Here, we propose a quantum analogue to K-means clustering, implement it on simulated superconducting qubits, and compare it to a previously developed quantum support vector machine. We find the algorithm's accuracy comparable to the classical K-means algorithm for clustering and classification problems, and find that it has asymptotic complexity $O(N^{3/2}K^{1/2}\log{P})$, where $N$ is the number of data points, $K$ is the number of clusters, and $P$ is the dimension of the data points, giving a significant speedup over the classical analogue.
翻译:机器学习算法因其多功能性而在许多不同的数据集中确定模式方面表现良好。 但是,随着数据集规模的扩大, 用于培训和使用这些统计模型的计算时间迅速增加。 量子计算提供了一个新的范例, 可能有能力克服这些计算困难。 在这里, 我们提议对 K 值分组进行量子类比, 在模拟超导QQbit 上实施, 并将其与先前开发的量子支持矢量机进行比较。 我们发现该算法的准确性与传统K 值组合和分类问题的计算方法相近, 并发现它具有微量复杂性$O( NQ3/2}K ⁇ 1/2 log{P} $, 其中美元是数据点的数量, $是数据组的数量, $是数据组的数量, $P$是数据点的维度, 在经典类比值上大大加快速度 。