Quantum Perceptron Revisited: Computational-Statistical Tradeoffs

Mathieu Roget, Giuseppe Di Molfetta, Hachem Kadri

Keywords: perceptron, quantum computing, Grover's search, generalization, computational-statistical tradeoff

Abstract: Quantum machine learning algorithms could provide significant speed-ups over their classical counterparts; however, whether they could also achieve good generalization remains unclear. Recently, two quantum perceptron models which give a quadratic improvement over the classical perceptron algorithm using Grover’s search have been proposed by Wiebe et al. [2016]. While the first model reduces the complexity with respect to the size of the training set, the second one improves the bound on the number of mistakes made by the perceptron. In this paper, we introduce a hybrid quantum-classical perceptron algorithm with lower complexity and better generalization ability than the classical perceptron. We show a quadratic improvement over the classical perceptron in both the number of samples and the margin of the data. We derive a bound on the expected error of the hypothesis returned by our algorithm, which compares favorably to the one obtained with the classical online perceptron. We use numerical experiments to illustrate the trade-off between computational complexity and statistical accuracy in quantum perceptron learning and discuss some of the key practical issues surrounding the implementation of quantum perceptron models into near-term quantum devices, whose practical implementation represents a serious challenge due to inherent noise. However, the potential benefits make correcting this worthwhile.

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