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Explicit Quantum Search Algorithm for the Densest k-Subgraph Problem

Year: 2026

Type: preprint

Abstract: This paper addresses the problem of finding the densest $k$-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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2604.27782

Authors: Biriukov, Yu. A., Morozov, R. D., Dyakonov, I. V., Straupe, S. S.

Institutions: Lomonosov Moscow State University, Russian Quantum Center

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: Russian Science Foundation, Foundation for the Advancement of Theoretical Physics and Mathematics

Awards: G1365167374, G2282574269

OpenAlex ID: W7159683112

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