Performance of Domain-Wall Encoding for Quantum Annealing

TL;DR

This paper experimentally compares domain-wall and one-hot encodings for discrete variables on quantum annealers, demonstrating the superior performance of domain-wall encoding across various metrics and problem sizes.

Contribution

It provides the first experimental validation showing domain-wall encoding outperforms one-hot encoding on quantum annealers for multiple problem types.

Findings

Domain-wall encoding outperforms one-hot encoding on current quantum annealers.

No single metric favors one-hot encoding over domain-wall.

A less connected quantum annealer with domain-wall encoding can outperform a more advanced one-hot system.

Abstract

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.