In computational biology, desired patterns are searched in large text databases, and an exact match is preferable. Classical benchmark algorithms obtain competent solutions for pattern matching in time, whereas quantum algorithm design is based on Grover's method, which completes the search in time. This paper briefly explains existing quantum algorithms and defines their processing limitations. Our initial work overcomes existing algorithmic constraints by proposing the quantum-based combined exact (QBCE) algorithm for the pattern-matching problem to process exact patterns. Next, quantum random access memory (QRAM) processing is discussed, and based on it, we propose the QRAM processing-based exact (QPBE) pattern-matching algorithm. We show that to find all occurrences of a pattern, the best case time complexities of the QBCE and QPBE algorithms are , and the exceptional worst case is bounded by . Thus, the proposed quantum algorithms achieve computational speedup. Our work is proved mathematically and validated with simulation, and complexity analysis demonstrates that our quantum algorithms are better than existing pattern-matching methods.

中文翻译：

---

基于量子的生物序列精确模式匹配算法

在计算生物学中，在大型文本数据库中搜索所需的模式，最好是精确匹配。经典基准算法及时获得模式匹配的有效解决方案，而量子算法设计基于格罗弗的方法，及时完成搜索。本文简要解释了现有的量子算法并定义了它们的处理限制。我们的初步工作通过针对模式匹配问题提出基于量子的组合精确 (QBCE) 算法来处理精确模式，从而克服了现有的算法约束。接下来，讨论了量子随机存取存储器（QRAM）处理，并在此基础上提出了基于QRAM处理的精确（QPBE）模式匹配算法。我们证明要找到所有出现模式时，QBCE 和 QPBE 算法的最佳情况时间复杂度为，异常最坏情况的时间复杂度为。因此，所提出的量子算法实现了计算加速。我们的工作在数学上得到了证明并通过模拟进行了验证，复杂性分析表明我们的量子算法优于现有的模式匹配方法。