Unconstrained binary models of the travelling salesman problem variants for quantum optimization

Abstract

Quantum computing is offering a novel perspective for solving combinatorial optimization problems. To fully explore the possibilities offered by quantum computers, the problems need to be formulated as unconstrained binary models, taking into account limitation and advantages of quantum devices. In this work, we provide a detailed analysis of the travelling salesman problem with time windows (TSPTW) in the context of solving it on a quantum computer. We introduce quadratic unconstrained binary optimization and higher-order binary optimization formulations of this problem. We demonstrate the advantages of edge-based and node-based formulations of the TSPTW problem. Additionally, we investigate the experimental realization of the presented methods on a quantum annealing device. The provided results pave the path for utilizing quantum computer for a variety of real-world tasks which can be cast in the form of travelling salesman problem with time windows.