Solving the traveling salesman problem on a quantum annealer

The paper contains an analysis of four software programs that solve the symmetric traveling salesman problem on a quantum annealer. Three are designed to find approximate solutions. One is designed to find an optimal tour. These programs demonstrate that an application can run across both classical and quantum computing platforms and take advantage of what each can do best. We add value by using a uniform structure for our analysis so that a consistent standard is used to evaluate the software programs. Also we add value by designing a software experiment to test the ability of the D-Wave quantum computer to optimally solve the traveling salesman problem. Our design combines the best attributes of the programs that are reviewed in this paper. Our design assumes that the variables of the traveling salesman problem can be embedded in the qubits, which excludes the problems in the TSP Library until the D-Wave Pegasus computer is available. We note applications of the asymmetric traveling salesman problem that are in the literature and include these problems in the recommendation for an experiment.