Fig. 7: Performance comparison between dimensional annealing and discrete spin simulation.
We use N = 40 spins and four random K graphs with adjacency matrices Ju with u = 1, …, 4. a Dependence of α2 on time t during the annealing. The vertical dashed gray lines mark the starting t0 and final annealing time tann. The insets depict the connectivity between any two XY spins (with negative coupling for illustration purposes). Here, α2 is the metric component along the y-axis, which is turned to zero at the end of the annealing. b Dynamics of the real PO amplitudes Xj from Eq. (5) with β = 10−2 during the annealing. After an initial dynamics, the POs corresponding to the y-components of the XY spins (dot-dashed lines) switch off, while the x-components reach a steady state (full lines, see Supplementary Movie 4). c–f Histograms of Ising success probability PIsing from the discrete spin simulation (D = 1, red histograms), and from the simulation of the XY model with annealing (interpolating between D = 2 and D = 1, blue histograms), as a function of the pump power deviation from threshold Δh/hth and for a given Ju as in the labels. As evident, the dimensional annealing significantly increases PIsing for a sufficiently large pump amplitude.
