Optimizing embedding-related quantum annealing parameters for reducing hardware bias

Quantum annealers have been designed to propose near-optimal solutions to NP-hard optimization problems. However, the accuracy of current annealers such as the ones of D-Wave Systems, Inc., is limited by environmental noise and hardware biases. One way to deal with these imperfections and to improve the quality of the annealing results is to apply a variety of pre-processing techniques such as spin reversal (SR), anneal offsets (AO), or chain weights (CW). Maximizing the effectiveness of these techniques involves performing optimizations over a large number of parameters, which would be too costly if needed to be done for each new problem instance. In this work, we show that the aforementioned parameter optimization can be done for an entire class of problems, given each instance uses a previously chosen fixed embedding. Specifically, in the training phase, we fix an embedding E of a complete graph onto the hardware of the annealer, and then run an optimization algorithm to tune the following set of parameter values: the set of bits to be flipped for SR, the specific qubit offsets for AO, and the distribution of chain weights, optimized over a set of training graphs randomly chosen from that class, where the graphs are embedded onto the hardware using E. In the testing phase, we estimate how well the parameters computed during the training phase work on a random selection of other graphs from that class. We investigate graph instances of varying densities for the Maximum Clique, Maximum Cut, and Graph Partitioning problems. Our results indicate that, compared to their default behavior, substantial improvements of the annealing results can be achieved by using the optimized parameters for SR, AO, and CW.