Performance of Domain-Wall Encoding for Quantum Annealing

In this article, we experimentally test the performance of the recently proposed domain-wall encoding of discrete variables Chancellor, 2019, 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 of both the problem and 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.