Sequence Alignment is the process of aligning biological sequences in order to identify similarities between multiple sequences. In this paper, a Quantum Algorithm for finding the optimal alignment between DNA sequences has been demonstrated which works by mapping the sequence alignment problem into a path-searching problem through a 2D graph. The transition, which converges to a fixed path on the graph, is based on a proposed oracle for profit calculation. By implementing Grover's search algorithm, our proposed approach is able to align a pair of sequences and figure out the optimal alignment within linear time, which hasn't been attained by any classical deterministic algorithm. In addition to that, the proposed algorithm is capable of quadratic speeding up to any unstructured search problem by finding out the optimal paths accurately in a deterministic manner, in contrast to existing randomized algorithms that frequently sort out the sub-optimal alignments, therefore, don't always guarantee of finding out the optimal solutions.

翻译：序列比对是将生物序列进行比对以识别多个序列间相似性的过程。本文提出一种量子算法，用于寻找DNA序列间的最优比对，其工作原理是将序列比对问题转化为通过二维图的路径搜索问题。该算法基于一个用于利润计算的提议oracle，其转换过程收敛于图上的固定路径。通过实现Grover搜索算法，我们提出的方法能够在线性时间内比对一对序列并找出最优比对，这是任何经典确定性算法都未曾达到的。此外，与现有经常筛选出次优比对的随机化算法（因此并不总能保证找到最优解）不同，所提算法能够通过确定性方式精确找出最优路径，从而对任何无结构搜索问题实现二次加速。