Impact of Fixing Spins in a Quantum Annealer with Energy Rescaling

TL;DR

This paper investigates how fixing spins combined with energy rescaling can improve the performance of quantum annealing, especially when size-reduction methods are used to handle large combinatorial problems.

Contribution

It explores the interplay between fixing spins and energy rescaling, demonstrating performance improvements through simulations and experiments on a quantum annealer.

Findings

Fixing spins enhances quantum annealing performance.

Energy rescaling preserves spin-chain embedding.

Method is effective for homogeneous, fully connected ferromagnetic Ising models.

Abstract

Quantum annealing is a promising algorithm for solving combinatorial optimization problems. However, various hardware restrictions significantly impede its efficient performance. Size-reduction methods provide an effective approach for addressing large-scale problems but often introduce additional challenges. A notable hardware restriction is the limited number of decision variables quantum annealing can handle compared to the size of the problem. Moreover, when employing size-reduction methods, the interactions and local magnetic fields in the Ising model--used to represent the combinatorial optimization problem--can become excessively large, making them difficult to implement on hardware. Although prior studies suggest that energy rescaling impacts the performance of quantum annealing, its interplay with size-reduction methods remains unexplored. This study examines the relationship between fixing spins, a promising size-reduction method, and the effects of energy rescaling. Numerical simulations and experiments conducted on a quantum annealer demonstrate that the fixing spins method enhances quantum annealing performance while preserving the spin-chain embedding for a homogeneous, fully connected ferromagnetic Ising model.