Quantum cluster algorithm for data classification

Junxu Li, Sabre Kais
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Abstract

We present a quantum algorithm for data classification based on the nearest-neighbor learning algorithm. The classification algorithm is divided into two steps: Firstly, data in the same class is divided into smaller groups with sublabels assisting building boundaries between data with different labels. Secondly we construct a quantum circuit for classification that contains multi control gates. The algorithm is easy to implement and efficient in predicting the labels of test data. To illustrate the power and efficiency of this approach, we construct the phase transition diagram for the metal-insulator transition of VO2, using limited trained experimental data, where VO2 is a typical strongly correlated electron materials, and the metallic-insulating phase transition has drawn much attention in condensed matter physics. Moreover, we demonstrate our algorithm on the classification of randomly generated data and the classification of entanglement for various Werner states, where the training sets can not be divided by a single curve, instead, more than one curves are required to separate them apart perfectly. Our preliminary result shows considerable potential for various classification problems, particularly for constructing different phases in materials.

用于数据分类的量子集群算法
我们提出了一种基于近邻学习算法的数据分类量子算法。分类算法分为两个步骤:首先,将同一类别的数据划分为具有子标签的更小的组,以帮助在具有不同标签的数据之间建立边界。其次,我们构建了一个包含多个控制门的量子分类电路。该算法易于实现,并能高效预测测试数据的标签。VO2 是一种典型的强相关电子材料,其金属-绝缘相变在凝聚态物理学中备受关注,为了说明这种方法的威力和效率,我们利用有限的训练实验数据构建了 VO2 的金属-绝缘相变图。此外,我们还在随机生成数据的分类和各种维尔纳态的纠缠分类上演示了我们的算法,在这些情况下,训练集不能用一条曲线来划分,而是需要多条曲线才能将它们完美地分开。我们的初步结果表明,在各种分类问题上,特别是在构建材料中的不同相位方面,我们具有相当大的潜力。
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期刊介绍: Journal of Materials Science: Materials Theory publishes all areas of theoretical materials science and related computational methods. The scope covers mechanical, physical and chemical problems in metals and alloys, ceramics, polymers, functional and biological materials at all scales and addresses the structure, synthesis and properties of materials. Proposing novel theoretical concepts, models, and/or mathematical and computational formalisms to advance state-of-the-art technology is critical for submission to the Journal of Materials Science: Materials Theory. The journal highly encourages contributions focusing on data-driven research, materials informatics, and the integration of theory and data analysis as new ways to predict, design, and conceptualize materials behavior.
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