Spin-1 quantum annealing with anisotropy-controlled intermediate-state pathways

TL;DR

This paper investigates spin-1 quantum annealing with anisotropy control, demonstrating that tunable anisotropy improves ground state fidelity by enabling smoother energy landscape traversal, thus offering advantages for ternary optimization problems.

Contribution

It introduces a spin-1 quantum annealing approach with anisotropy control, showing enhanced performance over traditional spin-1/2 systems due to intermediate states and adjustable anisotropy.

Findings

Higher fidelity in reaching ground states with suitable anisotropy D.

Intermediate spin levels facilitate incremental energy landscape traversal.

Anisotropy tuning stabilizes the annealing evolution.

Abstract

Quantum annealing offers a promising strategy for solving complex optimization problems by encoding the solution into the ground state of a problem Hamiltonian. While most implementations rely on spin-$1/2$ systems, we explore the performance of quantum annealing on a spin-$1$ system where the problem Hamiltonian includes a single ion anisotropy term of the form $D\sum (S^z)^2$. Our results reveal that for a suitable range of the anisotropy strength $D$, the spin-$1$ annealer reaches the ground state with higher fidelity. We attribute this performance to the presence of the intermediate spin level and the tunable anisotropy, which together enable the algorithm to traverse the energy landscape through smaller, incremental steps instead of a single large spin flip. This mechanism effectively lowers barriers in the configuration space and stabilizes the evolution. These findings suggest that higher spin annealers offer intrinsic advantages for robust and flexible quantum optimization, especially for problems naturally formulated with ternary decision variables.