D. Cai

The quantum approximate optimization algorithm (QAOA) is known for its capability and universality in solving combinatorial optimization problems on near-term quantum devices. The results yielded by QAOA depend strongly on its initial variational parameters. Hence, parameter selection for QAOA becomes an active area of research, as bad initialization might deteriorate the quality of the results, especially at great circuit depths. We first discuss the patterns of optimal parameters in QAOA in two directions: the angle index and the circuit depth. Then, we discuss the symmetries and periodicity of the expectation that is used to determine the bounds of the search space. Based on the patterns in optimal parameters and the bounds restriction, we propose a strategy that predicts the new initial parameters by taking the difference between the previous optimal parameters. Unlike most other strategies, the strategy we propose does not require multiple trials to ensure success. It only requires one prediction when progressing to the next depth. We compare this strategy with our previously proposed strategy and the layerwise strategy for solving the Max-cut problem in terms of the approximation ratio and the optimization cost. We also address the non-optimality in previous parameters, which is seldom discussed in other works despite its importance in explaining the behavior of variational quantum algorithms.

In this paper, we detect a magnetic null inside the MMS space‐craft (SC) tetrahedron using a linear interpolation that might be nearly impossible for very small inter‐SC separation like MMS (previously implemented on Cluster mission which is larger separation SC). We also report, successive or identical magnetic nulls that enter/reenter and cross the MMS spacecraft tetrahedron, and the “bifurcations” (change of the null type) of magnetic nulls are captured when it crosses one of four MMS tetrahedral surfaces during the 19 September 2015 event. During this event, we observe the eigenvalues of the radial null that enters and crosses the MMS tetrahedron changes from all real to one conjugate complex pair and one real eigenvalues, when the null exits through one of the tetrahedral boundary cells. This bifurcation is also evidenced by measuring the topological distance between two nulls before and after “bifurcation” using the Earth Mover's Distance.