AUTHOR=Mehta V. , Jin F. , Michielsen K. , De Raedt H. TITLE=On the hardness of quadratic unconstrained binary optimization problems JOURNAL=Frontiers in Physics VOLUME=10 YEAR=2022 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.956882 DOI=10.3389/fphy.2022.956882 ISSN=2296-424X ABSTRACT=

We use exact enumeration to characterize the solutions of quadratic unconstrained binary optimization problems of less than 21 variables in terms of their distributions of Hamming distances to close-by solutions. We also perform experiments with the D-Wave Advantage 5.1 quantum annealer, solving many instances of up to 170-variable, quadratic unconstrained binary optimization problems. Our results demonstrate that the exponents characterizing the success probability of a D-Wave annealer to solve a quadratic unconstrained binary optimization correlate very well with the predictions based on the Hamming distance distributions computed for small problem instances.