Traveling Salesman Problem in Quantum-Learning-Machine Approach

Abstract

Traveling salesman problem (TSP) is representative of combinatorial optimization problems in a certain class of hard problems so-called NP-complete problems. Finding an optimized solution to TSP is important, as it is associated with large number of scientific and engineering problems. In quantum information theory, some algorithms based on quantum physics guarantee higher efficiency than its classical counterparts. If a quantum algorithm for TSP is found, it is expected to show better efficiency than the classical. In particular, if such a quantum algorithm is of a polynomial time, TSP is reduced to a tractable problem. We have a long-term plan to develop quantum algorithms in a novel approach of quantum learning machine (QLM). In this paper, we propose a quantum-learning-machine approach in order to find a quantum algorithm for TSP.