A Classical Analogue of Quantum Annealing: From Anharmonic Oscillators to Spin-Glass Optimization

Finding the exact ground state of a spin-glass system is notoriously difficult. Experiments with the  D-Wave annealer indicate an anomalously slow decay of the residual energy with the  annealing time. To address this observation  we investigate a classical annealing protocol inspired by quantum annealing and study its performance across systems ranging from one-dimensional disordered chains to three-dimensional spin glasses. In ordered systems, the Kibble–Zurek mechanism predicts a power-law scaling of quantities such as the topological defect density with respect to the annealing time. We show that the algebraic scaling breaks down once disorder and frustration are present. They give rise instead to an inverse logarithmic behavior in the slow-annealing regime. We further analyze measurable quantities such as the residual energy to characterize the computational efficiency of this protocol, revealing universal features that may guide the design of classical and quantum optimization algorithms.