Minimum-length chain embedding for the phase unwrapping problem on D-Wave's advantage architecture

TL;DR

This paper introduces a new minimum-length chain embedding algorithm for quantum annealing on D-Wave's architecture, significantly improving phase unwrapping problem solutions by reducing chain lengths and enhancing performance.

Contribution

The paper presents a novel embedding algorithm that minimizes chain length for mapping phase unwrapping problems onto D-Wave's Pegasus graph, outperforming auto-embedding methods.

Findings

Lower chain lengths lead to better quantum annealing performance.

The new embedding algorithm outperforms D-Wave's auto-embedding.

The embedding can be applied to other problems on Pegasus graph.

Abstract

With the current progress of quantum computing, quantum annealing is being introduced as a powerful method to solve hard computational problems. In this paper, we study the potential capability of quantum annealing in solving the phase unwrapping problem, an instance of hard computational problems. To solve the phase unwrapping problem using quantum annealing, we deploy the D-Wave Advantage machine which is currently the largest available quantum annealer. The structure of this machine, however, is not compatible with our problem graph structure. Consequently, the problem graph needs to be mapped onto the target (Pegasus) graph, and this embedding significantly affects the quality of the results. Based on our experiment and also D-Wave's reports, the lower chain lengths can result in a better performance of quantum annealing. In this paper, we propose a new embedding algorithm that has the lowest possible chain length for embedding the graph of the phase unwrapping problem onto the Pegasus graph. The obtained results using this embedding strongly outperform the results of Auto-embedding provided by D-Wave. Besides the phase unwrapping problem, this embedding can be used to embed any subset of our problem graph to the Pegasus graph.