Exploring Replica Symmetry Breaking and Topological Collapse in Spin Glasses with Quantum Annealing

Replica symmetry breaking (RSB) underlies the complex organization of disordered systems, yet quantitative validation beyond N sim 100 spins has remained computationally challenging. We use quantum annealing to access ground states of the Sherrington-Kirkpatrick model up to N = 4000 spins, enabling the most extensive test of Parisi's Nobel Prize-winning RSB solution to date. Five independent observables confirm RSB predictions: ground-state energies converge to Parisi's value with characteristic N^-2/3 corrections, energy fluctuations scale as N^-3/4 $γ= 0.739 pm 0.036$, the chaos exponent θ= 0.51 pm 0.02 $R² = 0.989$ confirms mean-field universality, the overlap distribution exhibits hierarchical structure $σ_q = 0.19$, and the complexity remains invariant under 36% network dilution. Beyond a critical threshold 0.8 < D_c < 0.9, the hierarchy collapses discontinuously through a cooperative avalanche that converts the entire system to vacancies within a narrow parameter window ΔD = 0.1. These findings establish quantum computation as a tool for probing emergent many-body phenomena and uncover the topological foundations of complexity in disordered systems, with implications for neural networks, optimization, and materials science.