Minimum-Length Chain Embedding for the Phase Unwrapping Problem on D-Wave's Pegasus Graph

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 into the target (Pegasus) graph, and this minor 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 minor embedding algorithm that has the lowest possible chain length for minor 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 the D- Wave's minorminer tool both in the quality of the solution obtained and in the length of the chain.