Quantum AdaBoost with Supervised Learning Guarantee

Abstract

Although quantum algorithms based on parameterized quantum circuits promise to achieve quantum advantages, in the noisy intermediate-scale quantum (NISQ) era, their capabilities are greatly constrained due to limited number of qubits and depth of quantum circuits. Therefore, we may view these quantum algorithms as weak learners in supervised learning. Ensemble methods are a general technique in machine learning for combining weak learners to construct a more accurate one. In this paper, we theoretically prove and numerically verify a learning guarantee for quantum adaptive boosting (AdaBoost). To be specific, we theoretically depict how the prediction error of quantum AdaBoost on binary classification decreases with the increase of the number of boosting rounds and sample size. By employing quantum convolutional neural networks, we further demonstrate that quantum AdaBoost can not only achieve much higher accuracy in generalization and prediction, but also help mitigate the impact of noise. Our work indicates that in the current NISQ era, introducing appropriate ensemble methods is particularly valuable in improving the performance of quantum machine learning algorithms.