Although Durr and Hoyer have proposed state-of-the-art quantum algorithm (DHA) for searching minimum value, the lower limit of DHA’s successful probability is 1/2 . Also, DHA requires approximately \((\log _{2}N)^2\) copies of the initial state. In this paper, we propose a new quantum maximum or minimum searching algorithm (QUMMSA). In big data scenarios, according to sparse sampling with different densities, we can estimate the corresponding precision parameters. QUMMSA can improve the successful probability close to \(100\%\). Furthermore, with the quantum exact search algorithm, QUMMSA only requires approximately \(\log _2 N\) copies of the initial state to solve this problem. Since preparing an arbitrary quantum state is a problem with exponential complexity, our algorithm has a greater advantage with the increasing database size. In addition, we first propose a general method for circuits construction, which can be used in any database. An experiment implemented in an IBM superconducting processor and a numerical simulation of a 6-qubit system to solve a real issue indicate the feasibility and efficiency of QUMMSA. QUMMSA can serve as a subroutine in various quantum algorithms which involves searching maximum or minimum.

中文翻译：

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用于搜索最大值或最小值的低故障率量子算法

尽管Durr和Hoyer提出了最新的量子算法（DHA）来搜索最小值，但DHA成功概率的下限是1/2。此外，DHA需要大约\（（（log _ {2} N）^ 2 \）初始状态的副本。在本文中，我们提出了一种新的量子最大或最小搜索算法（QUMMSA）。在大数据场景中，根据不同密度的稀疏采样，我们可以估算出相应的精度参数。QUMMSA可以提高接近\（100 \％\）的成功概率。此外，使用量子精确搜索算法，QUIMMSA仅需要大约\（\ log _2 N \）副本的初始状态解决了这个问题。由于准备任意量子态是一个指数复杂的问题，因此随着数据库规模的增加，我们的算法具有更大的优势。另外，我们首先提出一种通用的电路构造方法，该方法可以在任何数据库中使用。在IBM超导处理器中进行的实验和一个6量子位系统的数值模拟解决了一个实际问题，表明了QUMMSA的可行性和效率。QUMMSA可以用作涉及搜索最大值或最小值的各种量子算法的子例程。