Fig 1.
Represention of the anneal schedules used as a function of the dimensionless anneal parameter s.
s = 1 indicates a fully annealed system. The reverse anneal schedule (blue) is parameterized by the reversal distance r and reversal time tr, while default forward anneal schedule (orange) increases from s = 0 to s = 1 over 20 μs.
Fig 2.
Calibration of the reverse anneal process.
Evaluated for 100 randomly chosen QUBOs appearing during an evaluation of the NBMF algorithm for with tr = 10μs and tr = 100μs. For a given reversal distance, the height of the green area indicates the mean probability that a reverse anneal sample will have a lower energy than the initial state. The heights of the red and blue areas indicate the mean probability that a given sample will be worse or the same, respectively, as the initial state. Standard deviations, not shown here, were upwards of 100% of the mean, however tr = 10μs and tr = 100μs always behaved similarly, and the peak reversal distance varied little from sample to sample.
Fig 3.
Comparison of forward and reverse anneal versions of the NBMF algorithm for fixed annealing time.
Mean performance reported from five evaluations of the forward and reverse annealing versions of the NBMF algorithm, with 1000 forward anneals and 240 reverse anneals per QUBO, corresponding to a total QPU access time of 6182 seconds over the full evaluation of each algorithm. Standard deviation (not shown) was less than 1% of the mean.
Fig 4.
Iterative improvement of B and C matrices for forward and reverse anneal versions of the NBMF algorithm.
Data taken during the evaluation of the algorithms as described in Fig 3.
Fig 5.
Comparison of forward and reverse anneal versions of NBMF algorithm after seven iterations for a range of annealing times.
Data taken from 725 distinct evaluations of the NBMF algorithm, varying the number of forward and reverse anneals per evaluation. Reverse annealing results in up to a 12% increase in performance.
Fig 6.
Comparison between Gurobi and reverse annealing.
The time required for Gurobi to find a solution that is as good as or better than the solution found by reverse annealing for each QUBO in a factorization problem is shown in comparison to the QPU access time and the annealing time. Cases where reverse annealing failed to find a better solution are excluded from the plot. In many cases, the time required by Gurobi exceeds both the annealing time and the QPU access time.