Quantum Algorithm for the Shortest Superstring Problem

TL;DR

This paper introduces a quantum algorithm for the Shortest Superstring Problem, achieving a running time of approximately 1.728^n, which is faster than classical approaches for sequence assembly tasks.

Contribution

The paper presents a novel quantum algorithm for SSP with a specific exponential time complexity, improving computational efficiency over classical methods.

Findings

Quantum algorithm runs in O*(1.728^n) time

Potential for faster DNA sequence assembly

Advances quantum approaches to combinatorial problems

Abstract

In this paper, we consider the ``Shortest Superstring Problem''(SSP) or the ``Shortest Common Superstring Problem''(SCS). The problem is as follows. For a positive integer $n$, a sequence of n strings $S=(s^1,\dots,s^n)$ is given. We should construct the shortest string $t$ (we call it superstring) that contains each string from the given sequence as a substring. The problem is connected with the sequence assembly method for reconstructing a long DNA sequence from small fragments. We present a quantum algorithm with running time $O^*(1.728^n)$. Here $O^*$ notation does not consider polynomials of $n$ and the length of $t$.