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

TL;DR

This study uses quantum annealing to validate Parisi's replica symmetry breaking in large spin glasses, revealing hierarchical organization, critical thresholds, and topological collapse, thus advancing understanding of complex disordered systems.

Contribution

First extensive quantum annealing validation of RSB in large spin glasses up to 4000 spins, demonstrating hierarchical structure and topological collapse phenomena.

Findings

Ground-state energies match Parisi's RSB predictions with finite-size corrections.

Energy fluctuations scale as N^{-3/4}, confirming mean-field universality.

Hierarchy collapses discontinuously at a critical dilution threshold.

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.