论文标题
量子提升
Quantum Boosting
论文作者
论文摘要
Suppose we have a weak learning algorithm $\mathcal{A}$ for a Boolean-valued problem: $\mathcal{A}$ produces hypotheses whose bias $γ$ is small, only slightly better than random guessing (this could, for instance, be due to implementing $\mathcal{A}$ on a noisy device), can we boost the performance of $ \ MATHCAL {a} $，以便在输入的$ 2/3 $上正确的$ \ Mathcal {a} $的输出是正确的吗？ 提升是一种将弱且不准确的机器学习算法转换为一种非常准确的学习算法的技术。 Freund和Schapire的Adaboost算法（2003年获得Gödel奖）是广泛使用的增强算法之一，在理论和实践中有许多应用。假设我们有一个$γ$的学习者，用于布尔概念类别$ c $，它需要时间$ r（c）$，然后是$ vc（c）\ cdot poly（r（c），1/γ）$的时间复杂性，其中$ vc（c）$是$ vc $ - vc $ dimmension $ c $ c $ $ c $。在本文中，我们展示了量子技术如何改善经典adaboost的时间复杂性。为此，假设我们有一个$γ$ weak量子量子学习者，用于布尔值概念$ c $，需要时间$ q（c）$，我们引入了一种量子增强算法，其复杂性缩放为$ \ sqrt {vc（c）} \ cdot poly（q（c），q（c），1/γ）; $ vc（c）$。
Suppose we have a weak learning algorithm $\mathcal{A}$ for a Boolean-valued problem: $\mathcal{A}$ produces hypotheses whose bias $γ$ is small, only slightly better than random guessing (this could, for instance, be due to implementing $\mathcal{A}$ on a noisy device), can we boost the performance of $\mathcal{A}$ so that $\mathcal{A}$'s output is correct on $2/3$ of the inputs? Boosting is a technique that converts a weak and inaccurate machine learning algorithm into a strong accurate learning algorithm. The AdaBoost algorithm by Freund and Schapire (for which they were awarded the Gödel prize in 2003) is one of the widely used boosting algorithms, with many applications in theory and practice. Suppose we have a $γ$-weak learner for a Boolean concept class $C$ that takes time $R(C)$, then the time complexity of AdaBoost scales as $VC(C)\cdot poly(R(C), 1/γ)$, where $VC(C)$ is the $VC$-dimension of $C$. In this paper, we show how quantum techniques can improve the time complexity of classical AdaBoost. To this end, suppose we have a $γ$-weak quantum learner for a Boolean concept class $C$ that takes time $Q(C)$, we introduce a quantum boosting algorithm whose complexity scales as $\sqrt{VC(C)}\cdot poly(Q(C),1/γ);$ thereby achieving a quadratic quantum improvement over classical AdaBoost in terms of $VC(C)$.
