Estimates of ground state energies for the quantum SK and 2D-EA model, using deGennes-Suzuki-Kubo mean-field annealing dynamics

Abstract

We perform a large scale simulation of quantum annealing in the Sherrington-Kirkpatrick (SK) spin glass up to a system size $N=40000$ to estimate its ground state energy using the deGennes-Suzuki-Kubo mean-field Ising dynamics, extending the earlier results (reported in Eur. Phys. J. B {\bf 98}, 226 (2025)). Here we numerically solve the deGennes-Suzuki-Kubo annealing dynamics to obtain the spin configurations and subsequently the ground state energy for a given system size at the end of the annealing (to the desired quantum system at the corresponding values of the transverse field), starting from a quantum paramagnetic state. The method shows high efficiency, with an overall algorithmic cost of $O(N^3)$ in estimating the energy of the ground state. We later extend this method to study the ground state energy of the Edwards-Anderson (EA) spin glass on a square lattice.