Quantum computation represents a computational paradigm whose distinctive attributes confer the ability to devise algorithms with asymptotic performance levels significantly superior to those achievable via classical computation. Recent strides have been taken to apply this computational framework in tackling and resolving various issues related to text processing. The resultant solutions demonstrate marked advantages over their classical counterparts. This study employs quantum computation to efficaciously surmount text processing challenges, particularly those involving string comparison. The focus is on the alignment of fixed-length substrings within two input strings. Specifically, given two input strings, $x$ and $y$, both of length $n$, and a value $d \leq n$, we want to verify the following conditions: the existence of a common prefix of length $d$, the presence of a common substring of length $d$ beginning at position $j$ (with $0 \leq j < n$) and, the presence of any common substring of length $d$ beginning in both strings at the same position. Such problems find applications as sub-procedures in a variety of problems concerning text processing and sequence analysis. Notably, our approach furnishes polylogarithmic solutions, a stark contrast to the linear complexity inherent in the best classical alternatives.

翻译：量子计算代表了一种计算范式，其独特属性赋予设计算法以超越经典计算所能达到的渐近性能水平的能力。近年来，人们已采取重要步骤将该计算框架应用于解决文本处理中的各种问题，所得结果相比经典方法展现出显著优势。本研究利用量子计算高效克服文本处理挑战，特别是涉及字符串比较的问题，重点关注两个输入字符串内固定长度子串的对齐。具体而言，给定两个长度均为$n$的输入字符串$x$和$y$，以及一个值$d \leq n$，我们需验证以下条件：长度为$d$的公共前缀的存在性、从位置$j$开始（$0 \leq j < n$）的长度为$d$的公共子串的存在性，以及两字符串在同一位置开始的任意长度为$d$的公共子串的存在性。这类问题作为子过程广泛应用于文本处理与序列分析中的多种场景。值得注意的是，我们的方法提供了多项式对数级别的解决方案，与最佳经典方案固有的线性复杂度形成鲜明对比。