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This study addresses the minor-embedding problem, which involves mapping thevariables of an Ising model onto a quantum annealing processor. The primarymotivation stems from the observed performance disparity of quantum annealerswhen solving problems suited to the processor's architecture versus those withnon-hardware-native topologies. Our research has two main objectives: i) toanalyze the impact of embedding quality on the performance of D-Wave Systemsquantum annealers, and ii) to evaluate the quality of the embeddings generatedby Minorminer, an algorithm provided by D-Wave and widely recognized as thestandard minor-embedding technique in the literature. Regarding the firstobjective, our experiments reveal a clear correlation between the average chainlength of embeddings and the relative errors of the solutions sampled. Thisunderscores the critical influence of embedding quality on quantum annealingperformance. For the second objective, we focus on the Minorminer technique,assessing its capacity to embed problems, the quality of the embeddingsproduced, and the robustness of the results. We also compare its performancewith Clique Embedding, another algorithm developed by D-Wave, which isdeterministic and designed to embed fully connected Ising models into quantumannealing processors, serving as a worst-case scenario. The results demonstratethat there is significant room for improvement for Minorminer, as it has notconsistently outperformed the worst-case scenario.

Addressing the Minor-Embedding Problem in Quantum Annealing and Evaluating State-of-the-Art Algorithm Performance