Quantum Ensemble for Classification

Abstract

A powerful way to improve performance in machine learning is to construct an ensemble that combines the predictions of multiple models. Ensemble methods are often much more accurate and have a lower variance than the individual classifiers that make them up, but have high requirements in terms of memory and computational time. In fact, a large number of alternative algorithms is usually adopted, each requiring to query all available data. We propose a new quantum algorithm that exploits quantum superposition, entanglement and interference to build an ensemble of classification models. Thanks to the generation of the several quantum trajectories in superposition, we obtain B transformations of the quantum state which encodes the training set in only log ( B ) operations. This implies an exponential growth of the ensemble size while increasing linearly the depth of the correspondent circuit. Furthermore, when considering the overall cost of the algorithm, we show that the training of a single weak classifier impacts additively to the overall time complexity rather than multiplicatively, as it usually happens in classical ensemble methods. We also present small-scale experiments on real-world datasets, defining a quantum version of the cosine classifier and using the IBM qiskit environment to show how the algorithms work.

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“…The angles in Figure5satisfy sin 𝛼 1 sin 𝛼 3 = − 1 24h 3 and cos 𝛼 1 cos 𝛼 2 cos 𝛼 3 = 8h 2 −1 8h 3 . Recently, a variational algorithm for quantum neural networks is proposed,[27] in which a general model framework to realize the quantum counterpart of the single hidden layer network is demonstrated. The investigation does not address how to implement the activation function and the framework supports plumbable activation function routines.…”