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 Jc between the qubits. Weak and strong Jc 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 Jcᵈᵉᶠᵃᵘˡᵗ, it is not an optimal coupling Jcᵒᵖᵗⁱᵐᵃˡ that maximizes the possible correct rate of QA measurements. In this paper, we present an algorithm how Jcᵒᵖᵗⁱᵐᵃˡ with the maximum probability p for observing the possible lowest energy is determined. Finally, we confirm that the extracted Jcᵒᵖᵗⁱᵐᵃˡ show much better p than Jcᵈᵉᶠᵃᵘˡᵗ 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.