Topological resilience of quantum coherence in Erdős–Rényi random graphs under edge dilution

Quantum coherence in many-body systems is typically fragile under structural disorder. While k-regular random graphs have been proposed as robust substrates due to their symmetry, they are vulnerable to edge deletion, which breaks resonance and triggers localization. Here, we investigate an alternative: Erdős–Rényi random graphs, which lack local regularity but exhibit strong statistical homogeneity. Using numerical simulations on systems of n=400 qubits, we study the evolution of the principal eigenstate under progressive random edge removal. By constructing ensemble-averaged density matrices, we find that ER-based networks maintain high state purity (Tr(ρ2)>0.95) even when only ∼40% of the original edges remain. In the low-connectivity regime, ER graphs outperform k-regular counterparts with matched average degree. This enhanced robustness arises not from symmetry, but from intrinsic spectral properties of random graphs—specifically, eigenvalue separation, eigenvector delocalization, and expander-like connectivity. The results suggest that statistical connectivity, rather than engineered regularity, can serve as a resource for fault-tolerant quantum state transport in disordered systems.