Paper: arXiv 2501.00075

Authors: Wei Li, Yi-Lun Du, Nan Su, Konrad Tywoniuk, Kyle Godbey, Horst Stöcker

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.

Complexity vs Empirical Score

  • Math Complexity: 5.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper applies a known quantum-inspired algorithm (Simulated Bifurcation) to community detection by formulating modularity maximization as a QUBO problem. While the mathematical mapping and algorithmic setup are solid, the empirical evaluation is limited to standard, small-scale toy benchmarks (Karate Club and IEEE 33-bus) without extensive financial backtesting or large-scale real-world financial network data.

Research Flowchart

  flowchart TD
    A[Research Goal: Solve NP-hard Community Detection using Quantum-Inspired SB] --> B[Formulate Problem as QUBO using Modularity Metric]
    B --> C[Input Benchmark Networks: Zachary's Karate Club & IEEE 33-bus]
    C --> D[Execute Simulated Bifurcation SB Algorithm]
    D --> E[Outcome: SB achieves highest modularity, matching Fujitsu DA]
    E --> F[Outcome: SB surpasses D-Wave and IBM Quantum Annealers]

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0 of 49 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.