Determination of Optimal Chain Coupling made by Embedding in D-Wave Quantum Annealer

The qubits in a D-wave quantum annealer (D-wave QA) are designed on a Pegasus graph that is different from structure of a combinatorial optimization problem. This situation requires embedding with the chains connected by ferromagnetic (FM) coupling $J_c$ between the qubits. Weak and strong $J_c$ values induce chain breaking and enforcement of chain energy, which reduce the accuracy of quantum annealing (QA) measurements, respectively. In addition, we confirmed that even though the D-Wave Ocean package provides a default coupling $J_c^{\text{default}}$, it is not an optimal coupling $J_c^{\text{optimal}}$ that maximizes the possible correct rate of QA measurements. In this paper, we present an algorithm how $J_c^{\text{optimal}}$ with the maximum probability $p$ for observing the possible lowest energy is determined. Finally, we confirm that the extracted $J_c^{\text{optimal}}$ show much better $p$ than $J_c^{\text{default}}$ in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems. The open code is available in \textit{https://github.com/HunpyoLee/OptimizeChainStrength}.