  Quantum annealers, such as the device built by D-Wave Systems, Inc., offer a
way to compute solutions of NP-hard problems that can be expressed in Ising or
QUBO (quadratic unconstrained binary optimization) form. Although such
solutions are typically of very high quality, problem instances are usually not
solved to optimality due to imperfections of the current generations quantum
annealers. In this contribution, we aim to understand some of the factors
contributing to the hardness of a problem instance, and to use machine learning
models to predict the accuracy of the D-Wave 2000Q annealer for solving
specific problems. We focus on the Maximum Clique problem, a classic NP-hard
problem with important applications in network analysis, bioinformatics, and
computational chemistry. By training a machine learning classification model on
basic problem characteristics such as the number of edges in the graph, or
annealing parameters such as D-Wave's chain strength, we are able to rank
certain features in the order of their contribution to the solution hardness,
and present a simple decision tree which allows to predict whether a problem
will be solvable to optimality with the D-Wave 2000Q. We extend these results
by training a machine learning regression model that predicts the clique size
found by D-Wave.
