  In this paper we experimentally test the performance of the recently proposed
domain-wall encoding of discrete variables from [Chancellor Quantum Sci.
Technol. 4 045004] on Ising model flux qubit quantum annealers. We compare this
encoding with the traditional one-hot methods and find that they outperform the
one-hot encoding for three different problems at different sizes both of the
problem and of the variables. From these results we conclude that the
domain-wall encoding yields superior performance against a variety of metrics
furthermore, we do not find a single metric by which one hot performs better.
We even find that a 2000Q quantum annealer with a drastically less connected
hardware graph but using the domain-wall encoding can outperform the next
generation Advantage processor if that processor uses one-hot encoding.
