Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem
Quantum Physics
2026-05-01 v1
Abstract
This paper addresses the problem of finding the densest -vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and bioinformatics. We propose two quantum approaches to solve this problem: reduction to Quadratic Unconstrained Binary Optimization (QUBO) and using Grover's quantum search algorithm. For the latter approach, we present an explicit gate-based oracle circuit utilizing Dicke states and Quantum Fourier Transform for edge counting. Numerical simulations demonstrate a quadratic speedup over classical Brute-force search.
Cite
@article{arxiv.2604.27782,
title = {Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem},
author = {Yu. A. Biriukov and R. D. Morozov and I. V. Dyakonov and S. S. Straupe},
journal= {arXiv preprint arXiv:2604.27782},
year = {2026}
}