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^default, it is not an optimal coupling J_c^optimal that maximizes the possible correct rate of QA measurements. In this paper, we present an algorithm how J_c^optimal with the maximum probability p for observing the possible lowest energy is determined. Finally, we confirm that the extracted J_c^optimal show much better p than J_c^default in QA measurements of various parameters of frustrated and fully connected combinatorial optimization problems. The open code is available in https://github.com/HunpyoLee/OptimizeChainStrength.