Comparison of D-Wave Quantum Annealing and Classical Simulated Annealing for Local Minima Determination

Restricted Boltzmann Machines trained with different numbers of iterations were used to provide a large diverse set of energy functions each containing many local valleys (LVs). They were used to confirm the property of the D-Wave quantum annealer (QA) to find potentially important LVs in the energy functions of Markov Random Fields that may be missed by classical searches. Even after a prohibitively long classical search by simulated annealing (SA), as many as 30-50% of the QA-found LVs remained not found by the SA. In order to establish if those LVs represent potentially important regions of the configuration space, they were compared to LVs that were found by both techniques. With respect to most of the important LV parameters, the LVs found only by the QA (missed by SA) were distributed in a wide range of the parameters' values. In an attempt to explain which LVs could not be found easily by the SA, it was established that for large or small, shallow or deep, wide or narrow LVs, the LVs found only by the QA are distinguished by a few-times smaller size of the LV basin of attraction (BoA). Apparently, the size of the BoA is much less important for QA search compared to the classical search, allowing QA to easily find many potentially important (e.g., wide and deep) LVs missed by even prohibitively lengthy classical searches.