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Systematic and deterministic graph minor embedding for Cartesian products of graphs

机译：系统和确定性图形的图形笛卡尔型产品的次要嵌入

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The limited connectivity of current and next-generation quantum annealers motivates the need for efficient graph minor embedding methods. These methods allow non-native problems to be adapted to the target annealer's architecture. The overhead of the widely used heuristic techniques is quickly proving to be a significant bottleneck for solving real-world applications. To alleviate this difficulty, we propose a systematic and deterministic embedding method, exploiting the structures of both the specific problem and the quantum annealer. We focus on the specific case of the Cartesian product of two complete graphs, a regular structure that occurs in many problems. We decompose the embedding problem by first embedding one of the factors of the Cartesian product in a repeatable pattern. The resulting simplified problem comprises the placement and connecting together of these copies to reach a valid solution. Aside from the obvious advantage of a systematic and deterministic approach with respect to speed and efficiency, the embeddings produced are easily scaled for larger processors and show desirable properties for the number of qubits used and the chain length distribution. We conclude by briefly addressing the problem of circumventing inoperable qubits by presenting possible extensions of our method.
机译：电流和下一代量子退化器的有限连接使得有必要有效的图表次要嵌入方法。这些方法允许非本地问题适应目标退化器的架构。广泛使用的启发式技术的开销很快被证明是解决现实世界应用的重要瓶颈。为了缓解这种困难，我们提出了一种系统和确定性的嵌入方法，利用特定问题和量子退化器的结构。我们专注于两个完整图表的笛卡尔乘积的具体情况，在许多问题中发生的常规结构。通过首先将笛卡尔产品的一个因素以可重复的模式嵌入其中一个因素来分解嵌入问题。由此产生的简化问题包括这些副本一起放置和连接以达到有效的解决方案。除了对速度和效率的系统和确定性方法的明显优点之外，生产的嵌入物很容易缩放较大的处理器，并为所使用的Qubits数量和链长分布表示期望的性质。通过介绍我们的方法可能的扩展，简要解决了避免无法操作的Qubits的问题来结束。

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