Community detection by simulated bifurcation

TL;DR

This paper demonstrates that the Simulated Bifurcation algorithm, inspired by quantum computing, effectively detects communities in complex networks, achieving high modularity and outperforming some quantum hardware solutions.

Contribution

The study introduces a quantum-inspired Simulated Bifurcation approach for community detection formulated as a QUBO problem, showing competitive results on benchmark networks.

Findings

SB achieved the highest modularity in benchmark tests.

SB matched Fujitsu's Digital Annealer performance.

SB outperformed D-Wave and IBM quantum machines.

Abstract

Community detection, also known as graph partitioning, is a well-known NP-hard combinatorial optimization problem with applications in diverse fields such as complex network theory, transportation, and smart power grids. The problem's solution space grows drastically with the number of vertices and subgroups, making efficient algorithms crucial. In recent years, quantum computing has emerged as a promising approach to tackling NP-hard problems. This study explores the use of a quantum-inspired algorithm, Simulated Bifurcation (SB), for community detection. Modularity is employed as both the objective function and a metric to evaluate the solutions. The community detection problem is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, enabling seamless integration with the SB algorithm. Experimental results demonstrate that SB effectively identifies community structures in benchmark networks such as Zachary's Karate Club and the IEEE 33-bus system. Remarkably, SB achieved the highest modularity, matching the performance of Fujitsu's Digital Annealer, while surpassing results obtained from two quantum machines, D-Wave and IBM. These findings highlight the potential of Simulated Bifurcation as a powerful tool for solving community detection problems.