Impact of Fixing Spins in a Quantum Annealer with Energy Rescaling

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 to addressing large-scale problems but often introduce additional difficulties. A notable hardware restriction is that quantum annealing can handle only a limited number of decision variables, 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.