Near-Term Quantum-Computing-Inspired Sampling for Community Detection in Low-Modularity Graphs (2509.03864v1)

Abstract: Low modularity networks (Q < 0.2) challenge classical community detection algorithms, which get trapped in local optima. We introduce quantum inspired community detection algorithms leveraging non classical sampling techniques to escape modularity optimization plateaus. Using distributions inspired by quantum phenomena including Porter Thomas distributions, Haar random states, and hyperuniform point processes, our approach generates diverse high quality partitions that improve modularity on difficult low Q graphs. We demonstrate 15 to 25% gains in modularity Q over classical methods (Louvain, Leiden). We define a "Modularity Recovery Gap" (MRG), the increase in Q achieved by quantum inspired refinement, and show this serves as a powerful anomaly detection signal. In experiments on high modularity networks (CTU 13 botnet traffic), MRG is near zero, confirming our method doesn't inflate modularity when no hidden structure exists. Results suggest quantum inspired sampling substantially enhances community detection in low modularity regimes, with applications in cybersecurity (stealthy APT/botnet detection), financial contagion modeling, disrupted supply chains, diseased brain connectomes, and crisis era social media analysis. Our refinements expand the search space of algorithms like Leiden without altering the graph, revealing partitions classical heuristics miss. While such partitions need not represent ground truth communities, they illustrate how near term quantum sampling can reshape optimization landscapes and enhance sensitivity to weak structure.