Performance of Domain-Wall Encoding for Quantum Annealing dataset

In this paper we experimentally test the performance of the recently proposed domain-wall en-coding of discrete variables from Chancellor Quantum Sci. Technol. 4 045004 on Ising model fluxqubit quantum annealers. We compare this encoding with the traditional one-hot methods and findthat they outperform the one-hot encoding for three different problems at different sizes both of theproblem and of the variables. From these results we conclude that the domain-wall encoding yieldssuperior performance against a variety of metrics furthermore, we do not find a single metric bywhich one hot performs better. We even find that a 2000Q quantum annealer with a drastically lessconnected hardware graph but using the domain-wall encoding can outperform the next generationAdvantage processor if that processor uses one-hot encoding.