标题： 量子算法用于有序目标的无结构搜索 显示英文标题

标题： Quantum algorithm for unstructured search of ranked targets

摘要： Grover的量子算法可以比任何经典算法更快地从非结构化数据库中找到一个标记项，因此已被用于密码分析和优化等多个应用。 当存在多个标记项时，Grover算法具有以均匀随机的方式找到其中一个的特性。 为了进一步扩展应用范围，它被推广为可以根据优先级按概率找到标记项，通过将优先级编码到Grover的oracle算子应用的振幅中。 在本文中，为了实现类似的推广，我们研究了一种不同的编码方式，将优先级整合到由oracle算子应用的相位中。 我们比较了之前的oracle算子和我们的oracle算子，并观察到哪一个表现更好取决于优先级参数。 由于优先级参数可以被视为Grover的oracle算子上的相关相位误差的大小，我们对oracle算子的分析也揭示了原始Grover算法对相关噪声的鲁棒性。 我们进一步通过数值计算表明，多个标记项之间的相干性会增加在使用我们的oracle算子的Grover算法中找到最优先项的概率。 显示英文摘要

摘要： Grover's quantum algorithm can find a marked item from an unstructured database faster than any classical algorithm, and hence it has been used for several applications such as cryptanalysis and optimization. When there exist multiple marked items, Grover's algorithm has the property of finding one of them uniformly at random. To further broaden the application range, it was generalized so that it finds marked items with probabilities according to their priority by encoding the priority into amplitudes applied by Grover's oracle operator. In this paper, to achieve a similar generalization, we examine a different encoding that incorporates the priority into phases applied by the oracle operator. We compare the previous and our oracle operators and observe that which one performs better depends on priority parameters. Since the priority parameters can be considered as the magnitude of the correlated phase error on Grover's oracle operator, the analysis of our oracle operator also reveals the robustness of the original Grover's algorithm against correlated noises. We further numerically show that the coherence between multiple marked items increases the probability of finding the most prioritized one in Grover's algorithm with our oracle operator.