Fig. 3: Influence of noise and eigenvalue dropout levels.

a–d Probability of finding the ground state, and the inverse of the autocorrelation time as a function of noise level ϕ for a sample Random Cubic Graph⁹ (N = 00, (50/100) eigenvalues (a), (99/100) eigenvalues (b), and a sample spin glass (N = 50, (37/100) eigenvalues (c), (26/100) eigenvalues (d)). The arrows indicate the estimated optimal noise level, from Eq. (8), taking \({\tau }_{{\rm{eq}}}^{E}\) to be constant. For this study we averaged the results of 100 runs of the PRIS with random initial states with error bars representing  ± σ from the mean over the 100 runs. We assumed Δ_ii = ∑_jK_ij. (e): N_{iter, 90%} versus noise level ϕ for these same graphs and eigenvalue dropout levels. f–g Eigenvalues of the transition matrix of a sample spin glass (N = 8) at ϕ = 0.5 (f) and ϕ= 2 (g). h The corresponding energy is plotted for various eigenvalue dropout levels α, corresponding to less than N eigenvalues kept from the original matrix. The inset is a schematic of the relative position of the global minimum when α = 1 (with (8/8) eigenvalues) with respect to nearby local minima when α < 1. For this study we assumed Δ_ii = ∑_jK_ij.