On quantum ensembles of quantum classifiers
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ORIGINAL ARTICLE
On quantum ensembles of quantum classifiers Amira Abbas1
· Maria Schuld1 · Francesco Petruccione1,2
Received: 2 February 2020 / Accepted: 1 May 2020 © Springer Nature Switzerland AG 2020
Abstract Quantum machine learning seeks to exploit the underlying nature of a quantum computer to enhance machine learning techniques. A particular framework uses the quantum property of superposition to store sets of parameters, thereby creating an ensemble of quantum classifiers that may be computed in parallel. The idea stems from classical ensemble methods where one attempts to build a stronger model by averaging the results from many different models. In this work, we demonstrate that a specific implementation of the quantum ensemble of quantum classifiers, called the accuracy-weighted quantum ensemble, can be fully dequantised. On the other hand, the general quantum ensemble framework is shown to contain the well-known Deutsch-Jozsa algorithm that notably provides a quantum speedup and creates the potential for a useful quantum ensemble to harness this computational advantage. Keywords Quantum machine learning · Quantum computing · Ensemble learning · Machine learning
1 Introduction An ensemble algorithm may be thought of as a model whose output considers the results generated from many models. The notion of ensembles dates as far back as early civilisations where majority voting was employed to make better decisions (Zhang and Ma 2012). One of the first ensemble methods proposed was Bayesian model averaging where one integrates (i.e. averages) over all possible parameters a model may contain to derive a solution (Hoeting et al. 1999). This allows for optimal predictive ability but an obvious problem is integrating over a possibly infinite parameter space, which is not always feasible (Madigan and Raftery 1994). This method, however, inspired the design of a quantum algorithm created Amira Abbas
[email protected] Maria Schuld [email protected] Francesco Petruccione [email protected] 1
Quantum Research Group, School of Chemistry and Physics, University of KwaZulu-Natal, Durban, KwaZulu-Natal, 4001, South Africa
2
National Institute for Theoretical Physics (NITheP), KwaZulu-Natal, 4001, South Africa
to replicate an ensemble framework (Chandra and Yao 2006; Hansen and Salamon 1990). An exponentially large ensemble of quantum classifiers are computed in parallel, weighed according to a specified weighing scheme, and their collective prediction is obtained through a single qubit measurement. The general routine is outlined in Schuld and Petruccione (2018) and termed the quantum ensemble of quantum classifiers. In a quantum machine learning setting, there is usually interplay between classical and quantum devices such as outsourcing difficult calculations to a quantum computer (Schuld and Killoran 2019; K¨ubler et al. 2019; Havl´ıcˇ ek et al. 2019; Benedetti et al. 2018), or classically optimising parameterised quantum algorithms (Peruzzo et al. 2014; Romero et al. 2017; Farhi et al. 2014; Verdon
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