Investigating the Chinese Postman Problem on a Quantum Annealer

TL;DR

This paper explores solving the Chinese Postman Problem using quantum annealing on D-Wave hardware, analyzing how hardware constraints affect solution quality and providing a formulation suitable for quantum optimization.

Contribution

It formulates the Chinese Postman Problem for quantum annealing and systematically analyzes hardware effects on solution success, bridging classical and quantum approaches.

Findings

Quantum annealing can solve the Chinese Postman Problem with hardware-aware embedding.

Embedding and spin-reversal controls influence solution probability.

Classical tabu algorithm provides a baseline comparison.

Abstract

The recent availability of quantum annealers has fueled a new area of information technology where such devices are applied to address practically motivated and computationally difficult problems with hardware that exploits quantum mechanical phenomena. D-Wave annealers are promising platforms to solve these problems in the form of quadratic unconstrained binary optimization. Here we provide a formulation of the Chinese postman problem that can be used as a tool for probing the local connectivity of graphs and networks. We treat the problem classically with a tabu algorithm and using a D-Wave device. We systematically analyze computational parameters associated with the specific hardware. Our results clarify how the interplay between the embedding due to limited connectivity of the Chimera graph, the definition of logical qubits, and the role of spin-reversal controls the probability of reaching the expected solution.