The quantum mechanical solution of the traveling salesman problem

A large category of important optimization problems in science and engineering comes down to the famous traveling salesman problem (or to its generalizations). We present a quantum mechanical solution that circumvents the necessity of a converging search strategy. On this score, we represent the edges of the graph as potential valleys and solve the two-dimensional Schrödinger equation for the entire landscape. At high quantum numbers we approach a classical path according to Bohrʹs correspondence principle, and then the principle of minimum action spontaneously favors the shortest tour. We display numerical examples, and we outline a practical realization on a hardware basis that might serve as a computer with a new design.