# Optimization Tests and Results¶

This section describes a set of tests and results that examine the quality of results returned by the optimization postprocessor. The goal is to describe the difference between postprocessed solutions from those obtained solely via the QPU.

Postprocessing for optimization is evaluated by generating 10 random problems on a D-Wave QPU, each with $J$ values drawn uniformly at random from $\{1, -1\}$. Each problem is evaluated based on a set of scaling factors. Problems are scaled to exaggerate the negative effects of analog noise on solution quality, so the optimization postprocessor can demonstrate that it can recover a high-quality solution from the QPU solution. Specifically, with small scaling factors, it is difficult to faithfully represent problems in the QPU because of the exaggeration of analog noise. This noise causes the solver to return lower-quality solutions, and provides a nice mechanism to evaluate the optimization postprocessor.

For each problem and scaling factor, 1000 samples were drawn with postprocessing on and off. As seen in Figure 112 and Figure 113, postprocessing for optimization can improve solutions significantly. Furthermore, the worse the non-postprocessed solutions are, the more postprocessing helps.

Fig. 112 Line plot of mean residual energies (mean energies above ground-state energy) returned by the D-Wave system with and without optimization postprocessing. Observe that optimization postprocessing does no harm, and helps more when scaling factors are smaller and the non-postprocessed samples not as good. Error bars indicate 95% confidence intervals over input Hamiltonians.

Fig. 113 Scatter plot of mean residual energies (mean energies above ground-state energy) returned by the D-Wave system with and without optimization postprocessing, with each point representing an input Hamiltonian. Observe that optimization postprocessing does no harm, and helps more when scaling factors are smaller and the non-postprocessed samples not as good.