Quantum Annealing (QA) can be used to quickly obtain near-optimal solutions for Quadratic Unconstrained Binary Optimization (QUBO) problems. In QA hardware, each decision variable of a QUBO should be mapped to one or more adjacent qubits in such a way that pairs of variables defining a quadratic term in the objective function are mapped to some pair of adjacent qubits. However, qubits have limited connectivity in existing QA hardware. This has spurred work on preprocessing algorithms for embedding the graph representing problem variables with quadratic terms into the hardware graph representing qubits adjacencies, such as the Chimera graph in hardware produced by D-Wave Systems. In this paper, we use integer linear programming to search for an embedding of the problem graph into certain classes of minors of the Chimera graph, which we call template embeddings. One of these classes corresponds to complete bipartite graphs, for which we show the limitation of the existing approach based on minimum Odd Cycle Transversals (OCTs). One of the formulations presented is exact, and thus can be used to certify the absence of a minor embedding using that template. On an extensive test set consisting of random graphs from five different classes of varying size and sparsity, we can embed more graphs than a state-of-the-art OCT-based approach, our approach scales better with the hardware size, and the runtime is generally orders of magnitude smaller.

翻译：在 QA 硬件中, QUBO 的每个决定变量应映射为一个或多个相邻的quitits 。 在本文中, 我们使用整数线编程来寻找将问题图嵌入Chimera 图形的某些类别, 我们称之为模板嵌入。 这些类别之一与完整的双向硬度图相匹配, 我们从中可以展示基于最小正方位的正方位缩放比例表的现有方法的局限性, 并且可以显示基于最小正方位的正方位缩放比例表的当前方法的局限性。 在本文中, 我们使用整数线性编程将问题图嵌入Chimera 函数中某些类型的未成年人, 我们称之为模板嵌入。 这些类别之一与完整的双向量度图相匹配, 我们用最小正方位变形变形变形变形变形变形变形变形变形变形图显示基于最小正方位变形变形变形变形变形变形变形图的当前方法的局限性。