Effects of Graph Network Connections on The Efficiency of Quantum Annealing

TL;DR

This paper investigates how different graph structures and interaction types affect the efficiency of quantum annealing, revealing that interaction choice and connectivity significantly influence performance and energy gaps.

Contribution

It compares the effects of Ising, Heisenberg XY, and anisotropic exchange interactions on QA across various graph structures, highlighting their impact on performance and energy gaps.

Findings

Ising model performance is less affected by graph structure variations.

Heisenberg XY suffers performance loss with increased connectivity.

Anisotropic exchange interactions are impractical for complete graphs.

Abstract

Graph structure of quantum spin networks plays an essential role in applying quantum annealing (QA). The Ising model is the typical choice to describe the interactions between the spins in the networks. Here, we explore the interplay of different interaction types between the spins and the structure of the underlying network on the performance of QA. Specifically, we consider the Heisenberg XY and antisymmetric anisotropic exchange interaction models, in addition to the usual Ising Model, in graph structures ranging from linear chains to complete graphs with different connectivities. We find that the QA performance of the Ising model shows less variation with the change of graph structure among different interaction types. The Heisenberg XY model suffers from significant performance losses with increasing connections beyond linear chains, which we attribute to increasing entropy built-up. Anisotropic exchange interactions turn out to be an impractical choice for complete graphs due to the diminishing energy gap during annealing. Furthermore, we investigate the effect of inhomogeneous couplings and reveal a trade-off between coupling strength and performance, especially significant for the case of the anisotropic exchange model.