量子感知器再访：计算-统计权衡
Quantum Perceptron Revisited: Computational-Statistical Tradeoffs
摘要：
量子机器学习算法可以提供比经典算法更快的速度;然而，它们是否也可以实现良好的泛化仍然不清楚。最近，Wiebe等人提出了两个量子感知器模型，它们使用Grover搜索对经典感知器算法进行了二次改进。虽然第一个模型降低了训练集大小的复杂性，但第二个模型提高了感知器错误数量的界限。本文提出了一种量子-经典混合感知器算法，该算法比经典感知器具有更低的复杂度和更好的泛化能力。我们表现出一个二次改进的经典感知器的样本数量和利润率的数据。我们推导出一个约束的假设返回我们的算法，这与经典的在线感知器得到的相比毫不逊色的预期误差。我们使用数值实验来说明量子感知器学习中计算复杂性和统计准确性之间的权衡，并讨论了将量子感知器模型实现为近期量子设备的一些关键实际问题，由于固有的噪声，其实际实现是一个严峻的挑战。然而，潜在的好处使纠正这一点值得。
英文摘要：
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. arXiv:1602.04799 . 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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