The D-wave quantum annealer requires embedding with ferromagnetic (FM) chains connected by several qubits, because it cannot capture exact long-range coupling between qubits, and retains the specific architecture that depends on the hardware type. Therefore, determination of the chain strength $J_c$ required to sustain FM order of qubits in the chains is crucial for the accuracy of quantum annealing. In this study, we devise combinatorial optimization problems with ordered and disordered qubits for various embeddings to predict appropriate $J_c$ values. We analyze the energy interval $\Delta_s$ and $\Delta_c$ between ground and first excited states in the combinatorial optimization problems without and with chains respectively, using the exact approach. We also measure the probability $p$ that the exact ground energy per site $E_g$ is observed in many simulated annealing shots. We demonstrate that the determination of $J_c$ is increasingly sensitive with growing disorder of qubits in the combinatorial optimization problems. In addition, the values of appropriate $J_c$, where the values of $p$ are at a maximum, increase with decreasing $\Delta_s$. Finally, the appropriate value of $J_c$ is shown to be observed at approximately $\Delta_c/\Delta_s=0.25$ and $2.1 E_g$ in the ordered and disordered qubits, respectively.

中文翻译：

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在 D-Wave 量子退火炉中确定嵌入引起的链强度

D 波量子退火器需要嵌入由多个量子位连接的铁磁 (FM) 链，因为它无法捕获量子位之间的精确远程耦合，并保留取决于硬件类型的特定架构。因此，确定维持链中量子比特的 FM 顺序所需的链强度 $J_c$ 对于量子退火的准确性至关重要。在这项研究中，我们为各种嵌入设计了有序和无序量子比特的组合优化问题，以预测适当的 $J_c$ 值。我们使用精确的方法分别分析了没有链和有链的组合优化问题中基态和第一激发态之间的能量区间 $\Delta_s$ 和 $\Delta_c$。我们还测量了在许多模拟退火镜头中观察到每个站点的确切地面能量 $E_g$ 的概率 $p$。我们证明了$J_c$ 的确定随着组合优化问题中量子比特的无序程度的增加而变得越来越敏感。此外，适当的 $J_c$ 的值（其中 $p$ 的值最大）随着 $\Delta_s$ 的减小而增加。最后，在有序和无序量子比特中，分别在大约 $\Delta_c/\Delta_s=0.25$ 和 $2.1 E_g$ 处观察到 $J_c$ 的适当值。随着 $\Delta_s$ 的减少而增加。最后，在有序和无序量子比特中，分别在大约 $\Delta_c/\Delta_s=0.25$ 和 $2.1 E_g$ 处观察到 $J_c$ 的适当值。随着 $\Delta_s$ 的减少而增加。最后，在有序和无序量子比特中，分别在大约 $\Delta_c/\Delta_s=0.25$ 和 $2.1 E_g$ 处观察到 $J_c$ 的适当值。