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.
Highlights
Machine learning techniques have demonstrated remarkable success in numerous topics in science and engineering, including artificial intelligence (Mitchell et al 1990; Duda et al 1973), molecular dynamics (Botu and Ramprasad 2015), light harvesting systems (Häse et al 2017), molecular electronic properties (Montavon et al 2013), surface reaction network (Ulissi et al 2017), density functional models (Brockherde et al 2017), phase classification, and quantum simulations (Wang 2016; Carrasquilla and Melko 2017; Broecker et al 2017; Ch’Ng et al 2017; Van Nieuwenburg et al 2017; Arsenault et al 2014; Kusne et al 2014)
Modern machine learning techniques have been applied to the state space of complex condensed-matter systems for their abilities to analyze exponentially large data sets (Carrasquilla and Melko 2017), speed-up searches for novel energy generation/storage materials (De Luna et al 2017; Wei et al 2016) and classification of entanglement (Gao et al 2018)
Researchers have succeeded to apply quantum machine learning algorithms to various systems such as superconducting circuits (Havlícek et al 2019) and photonic systems (Cai et al 2015), which leads to enormous enthusiasm applying quantum algorithms into various areas (Xia and Kais 2018; Hu et al 2020; 2020; Li et al 2021; Xia et al 2017; Sajjan et al 2021; Xia et al 2021)
Summary
Machine learning techniques have demonstrated remarkable success in numerous topics in science and engineering, including artificial intelligence (Mitchell et al 1990; Duda et al 1973), molecular dynamics (Botu and Ramprasad 2015), light harvesting systems (Häse et al 2017), molecular electronic properties (Montavon et al 2013), surface reaction network (Ulissi et al 2017), density functional models (Brockherde et al 2017), phase classification, and quantum simulations (Wang 2016; Carrasquilla and Melko 2017; Broecker et al 2017; Ch’Ng et al 2017; Van Nieuwenburg et al 2017; Arsenault et al 2014; Kusne et al 2014). Researchers have succeeded to apply quantum machine learning algorithms to various systems such as superconducting circuits (Havlícek et al 2019) and photonic systems (Cai et al 2015), which leads to enormous enthusiasm applying quantum algorithms into various areas (Xia and Kais 2018; Hu et al 2020; 2020; Li et al 2021; Xia et al 2017; Sajjan et al 2021; Xia et al 2021)
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