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

Abstract

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 $N^{-3/4}$ ($\gamma = 0.739 \pm 0.036$), the chaos exponent $\theta = 0.51 \pm 0.02$ ($R^2 = 0.989$) confirms mean-field universality, the overlap distribution exhibits hierarchical structure ($\sigma_q = 0.19$), 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 $\Delta D = 0.1$. 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.