Comprehensive Validation of Replica Symmetry Breaking via Quantum Annealing: From Ground States to Topological Collapse

Abstract: Giorgio Parisi's exact solution of the Sherrington-Kirkpatrick spin glass, recognized with the 2021 Nobel Prize in Physics, revealed revolutionary hierarchical organization in disordered systems, yet systematic validation has remained computationally intractable beyond $N \sim 100$ spins, and the topological limits of this complexity remain unexplored. Here we leverage quantum annealing to extend ground-state computations to 4000 spins and systematically probe both the emergence and breakdown of replica symmetry breaking. Three independent measurements validate core RSB predictions: ground-state energies converge to Parisi's value $E_\infty/N = -0.7633$ with predicted $N^{-2/3}$ finite-size corrections; chaos exponent $\theta = 0.51 \pm 0.02$ confirms mean-field square-root scaling ($R^2 = 0.989$); and state-space overlap distribution exhibits broad continuous structure ($\sigma_q = 0.19$) characteristic of hierarchical landscape organization. We then investigate RSB robustness by introducing controlled network dilution via the Blume-Capel model with vacancy formation. Remarkably, hierarchical complexity remains invariant under 36\% dilution, proving RSB is a topological property of network connectivity rather than spin density. Beyond a critical threshold in the range $0.8 < D_c < 0.9$, the hierarchy collapses discontinuously as the system undergoes complete conversion to the all-vacancy state within a narrow parameter window an abrupt avalanche-driven transition where independent-vacancy mean-field theory correctly predicts the energy scale but fails to capture the cooperative dynamics. This comprehensive validation across thermodynamics, universality, landscape geometry, and topological limits establishes quantum advantage for probing fundamental statistical mechanics in complex systems relevant to neural networks, optimization, and materials science.