  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.
