A significant challenge in quantum annealing is to map a real-world problem onto a hardware graph of limited connectivity. When the problem graph is not a subgraph of the hardware graph, one might employ minor embedding in which each logical qubit is mapped to a tree of physical qubits. Pairwise interactions between physical qubits in the tree are set to be ferromagnetic with some coupling strength \(F<0\). Here we address the theoretical question of what the best value F should be in order to achieve unbroken trees in the pre-quantum-processing. The sum of |F| for each logical qubit is defined as minor embedding energy, and the best value F is obtained when the minor embedding energy is minimized. We also show that our new analytical lower bound on |F| is a tighter bound than that previously derived by Choi (Quantum Inf Process 7:193–209, 2008). In contrast to Choi’s work, our new method depends more delicately on minor embedding parameters, which leads to a higher computational cost.

中文翻译：

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最小化较小的嵌入能：在量子退火中的应用

量子退火中的一个重大挑战是将现实问题映射到连接受限的硬件图上。当问题图不是硬件图的子图时，可以采用次要嵌入，其中每个逻辑量子位都映射到一棵物理量子位。树中物理量子位之间的成对相互作用被设置为具有一定耦合强度\（F <0 \）的铁磁性。在这里，我们讨论理论上的问题，即在预量子处理中，要达到不间断的树，最佳值F应该是多少。|的总和 F | 每个逻辑量子位定义为较小的嵌入能量，并且最佳值为F当较小的嵌入能量最小化时获得。我们还显示了| F | 与Choi先前推导的约束相比，约束更严格（Quantum Inf Process 7：193–209，2008）。与Choi的工作相反，我们的新方法更加精细地依赖于较小的嵌入参数，这导致更高的计算成本。