Effects of Graph Network Connections on The Efficiency of Quantum Annealing

Abstract

Graph structure of quantum spin networks plays an important role in the applications of quantum annealing. In this work, we compare the performance results of four basic graph structures. Generally, the interaction model choice for quantum annealing is Ising but we test Hamilton XY and antisymmetric anisotropic models as well. Major findings include that Ising model interactions are the most persistent with the change of graph structure. Heisenberg XY model suffers from performance losses with highly connected square graphs which can be attributed to large entropy built-up. Whereas anisotropic model is impractical with square type graphs as energy gap calculations approach zero during annealing. Furthermore, inhomogeneous couplings and their effects on different models and graph structures show a trade-off between coupling strength and performance especially in the case of the anisotropic model.