Effects of Graph Network Connections on The Efficiency of Quantum Annealing
arXiv:2111.11411
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.
arXiv comment7 pages, 5 figures, corrections of typos and grammar, added analysis in subsection anisotropic coupling, added reference for coherence results, updated abstract, introduction, and conclusions
References in corpus (14)
- Quantifying Coherence
- Quantum Annealing in the Transverse Ising Model
- Adiabatic Quantum Computing
- Theory of Quantum Annealing of an Ising Spin Glass
- Quantum Annealing and Analog Quantum Computation
- Quantum fidelity measures for mixed states
- Flight Gate Assignment with a Quantum Annealer
- A quantum annealer with fully programmable all-to-all coupling via Floquet engineering
- Graph isomorphism and adiabatic quantum computing
- Steering random spin systems to speed up the quantum adiabatic algorithm
- Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems
- Disorder-assisted graph coloring on quantum annealers
- Entanglement as a resource in adiabatic quantum optimization
- Singular-value decomposition using quantum annealing