Fig 1.
Digits of accuracy plotted against number of iterations.
Total annealing time is the total amount of time the algorithm spends on performing SA, since SA dominates the cost of the method. Evec error is the distance of the computed vector from the true unit eigenvector. Precision refers to the scaling applied to the discretized cube at each iteration. The initial guess phase corresponds to a precision of 1. Observe that whenever the error increases, the algorithm responds by increasing the precision, which often gives large accuracy gains within the subsequent 2-3 iterations.
Fig 2.
Error plot for 560 × 560 space Shuttle control matrix.
Fig 3.
Error plots for generalized eigenvalue problem on two 48 × 48 mesh matrices.
Fig 4.
Eigenvector error for MP matrices at the end of initial guess phase.
Observe that for small QUBOs the full response decreases the error significantly.
Fig 5.
Average number of iterations required for MP matrices for different parameters.
Fig 6.
Total iterations required for different initializations of λ.
Fig 7.
Average number of iterations on 30 samples as a function of the gap size |λ1 − λ2|.
The smaller the gap, the more iterations required, especially when the number of bits is small. In the extreme case where the gap is 0 and the lowest eigenvalue appears with multiplicity, the algorithm is actually faster in the sense that fewer iterations are needed for the computed eigenvalue to approximate the true eigenvalue.
Fig 8.
Sample plots for two 10 × 10 matrices with gap size .1 and .01.
As the gap size decreases, the ratio of eigenvector error to precision and eigenvalue error increases.
Fig 9.
Average number of iterations running the algorithm twice on matrices with complete degeneracy.
One can see slightly better performance on the second run, particularly on the 20 × 20 matrices.