A quantum algorithm for pairwise sequence alignment

Abstract

DNA Sequence Alignment is the process of aligning DNA sequences in order to identify similarities between multiple sequences. The primary reason is to sort out the evo lutionary, functional or structural relationships within sequences. In our thesis, we are trying to design a Quantum Algorithm for finding the optimal alignments between DNA sequences. This particular method of finding DNA sequences works by mapping the se quence alignment problem to a path searching problem through a 2D graph. The tran sition which converges to a fixed path on the graph is based on a proposed oracle for profit calculation. In order to generate a graph and create random paths through it, we searched and analyzed several Quantum Walk Algorithms to align sequences in contrast to classical random walk search algorithms. Our primary goal is to align DNA sequences and find the optimal alignments in a faster and efficient way with Grover’s search algo rithm. It is capable of quadratic speeding up of any unstructured search problem. The intent here is to provide a comprehensive elaboration of how path searching algorithm works on DNA sequences according to a quantum algorithm.