Quantum algorithm for de novo DNA sequence assembly based on quantum walks on graphs

TL;DR

This paper presents a quantum algorithm leveraging quantum walks on graphs to improve de novo DNA sequence assembly, addressing the NP-hard path-finding challenge with hierarchical graph partitioning and quantum path search methods.

Contribution

It introduces a novel quantum algorithm that combines hierarchical graph partitioning with quantum walks to efficiently find paths in overlap graphs for DNA assembly.

Findings

Successfully tested quantum algorithms using Qiskit.

Demonstrated hierarchical partitioning reduces problem complexity.

Proposed approach may lead to more efficient DNA assembly algorithms.

Abstract

De novo DNA sequence assembly is based on finding paths in overlap graphs, which is a NP-hard problem. We developed a quantum algorithm for de novo assembly based on quantum walks in graphs. The overlap graph is partitioned repeatedly to smaller graphs that form a hierarchical structure. We use quantum walks to find paths in low rank graphs and a quantum algorithm that finds Hamiltonian paths in high hierarchical rank. We tested the partitioning quantum algorithm, as well as the quantum algorithm that finds Hamiltonian paths in high hierarchical rank and confirmed its correct operation using Qiskit. We developed a custom simulation for quantum walks to search for paths in low rank graphs. The approach described in this paper may serve as a basis for the development of efficient quantum algorithms that solve the de novo DNA assembly problem.