In this paper, we study Quantum Abstract Detecting Systems (QADS), that generalize some key characteristics of the operators used in Grover’s algorithm, a wide variety of quantum walks and the quantum abstract search algorithm. A QADS is an algorithm that constructs a quantum state and a quantum operator that help testing whether a circuit-implemented boolean function f is identically zero. We also identify some relatively weak properties of QADS that lead to the construction of algorithms for the detection problem (i.e. determining whether there is a marked element in a given set). Our results provide not only a common framework to all the aforementioned search methods, and their transformation into algorithms for the detection problem, but also allow the development of new similar methods. As an example, we construct a modification of Grover’s algorithm (from the tensor product of controlled QADS) that shows improved detection probability.

中文翻译：

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量子抽象检测系统

在本文中，我们研究了量子抽象检测系统（QADS），该系统概括了Grover算法，各种量子步态和量子抽象搜索算法中使用的算子的一些关键特性。QADS是一种构造量子状态和量子算符的算法，可帮助测试电路实现的布尔函数f等于零。我们还确定了QADS的一些相对较弱的属性，这些属性导致构造了检测问题的算法（即，确定给定集中是否存在标记元素）。我们的结果不仅为所有上述搜索方法提供了一个通用框架，而且将其转换为用于检测问题的算法，还允许开发新的类似方法。例如，我们构造了Grover算法的一种修改形式（从受控QADS的张量积中得出），该算法显示出更高的检测概率。