Algorithms that search for a pattern within a larger data-set appear ubiquitously in text and image processing. Here, we present an explicit, circuit-level implementation of a quantum pattern-matching algorithm that matches a search string (pattern) of length M inside a longer text of length N. Our algorithm has a time complexity of \(\tilde{O}(\sqrt{N})\), while the space complexity remains modest at O(N + M). We report the quantum gate counts relevant for both pre-fault-tolerant and fault-tolerant regimes.

中文翻译：

---

字符串匹配的量子算法

在较大的数据集中搜索模式的算法在文本和图像处理中无处不在。在这里，我们提出了一种量子模式匹配算法的显式电路级实现，该算法在长度为N的较长文本内匹配长度为M的搜索字符串（模式）。我们的算法的时间复杂度为\（\ tilde {O}（\ sqrt {N}）\），而空间复杂度保持为O（N  +  M）。我们报告了与容错前和容错机制相关的量子门计数。