Kernel methods in Quantum Machine Learning
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Kernel methods in Quantum Machine Learning Riccardo Mengoni1 · Alessandra Di Pierro1 Received: 28 April 2019 / Accepted: 22 September 2019 © Springer Nature Switzerland AG 2019
Abstract Quantum Machine Learning has established itself as one of the most promising applications of quantum computers and Noisy Intermediate Scale Quantum (NISQ) devices. In this paper, we review the latest developments regarding the usage of quantum computing for a particular class of machine learning algorithms known as kernel methods. Keywords Quantum Machine Learning · Quantum computing · Kernel methods
1 Introduction In the era of big data, Machine Learning (ML) provides a set of techniques to identify patterns among huge datasets “without being explicitly programmed to perform that task” (Bishop 2016; Mitchell 1997). In the last few years, building on the great success of ML, a new interdisciplinary research topic going under the name of Quantum Machine Learning (QML) has emerged (Schuld 2015; Wittek 2014; Biamonte et al. 2017; Ciliberto et al. 2018; Dunjko and Briegel 2018; Arunachalam and Wolf 2017; Perdomo-Ortiz et al. 2018; Schuld and Petruccione 2018). The aim of QML is to merge in different ways quantum computing and data mining techniques in order to achieve improvements in both fields. As shown in Fig. 1, it is possible to distinguish four approaches to QML, depending on the nature of the dataset under study and the computation device being used (Dunjko et al. 2016). The Classical-Classical (CC) class refers to ordinary machine learning or to machine learning algorithms that are inspired by the formalism of quantum mechanics. Here the dataset represents some classical system and the algorithm can run on a classical computer (Dong et al. 2019; Canabarro et al. 2019; Amin et al. 2018; Crawford et al. 2016;
Riccardo Mengoni
[email protected] Alessandra Di Pierro [email protected] 1
Department of Informatics, University of Verona, Verona, Italy
Stoudenmire and Schwab 2016; Sergioli et al. 2018; Levine et al. 2018). In the Classical-Quantum (CQ) class, algorithms rely on the advantages of quantum computation in order to speed up classical ML methods. Data are assumed to be classical in this class as well (A¨ımeur et al. 2013; Mikhail et al. 2016; Wiebe et al. 2015; Barry et al. 2014; Lu and Braunstein 2014; Heim et al. 2015; Bottarelli et al. 2018). Quantum-Classical (QC) refers to the use of classical ML methods to analyse quantum systems (Agresti et al. 2019; Huembeli et al. 2019; Gray et al. 2018; Benedetti et al. 2019; Di Pierro et al. 2018; O’Driscoll et al. 2019; Iten et al. 2018). Finally, in the Quantum-Quantum (QQ) class, both the learning algorithm and the system under study are fully quantum (Yu et al. 2019). Some very promising results have been obtained relatively to each of the four frameworks. In this paper, we have chosen to focus on the CQ section with the aim to review the main approaches that use quantum mechanics in order to obtain a computational advantage for a speci
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