Employing continuous quantum systems to solve optimization problems

Abstract

At land, sea and in the air mobility and traffic management offer a vast amount of problems with a large potential of optimization with quantum computers, e.g. service scheduling, route planning, or path optimization. Many of these problems can be described at a fundamental level by the traveling salesman problem (TSP), in which the shortest route while visiting each point exactly once is to be found [1]. The TSP has already received a lot of attention in the quantum computing community, for example, implementations for adiabatic quantum annealers exist and have been tested [2,3]. We investigate the TSP with a focus on going beyond qubits by employing continuous quantum systems. Using bosonic Qiskit we simulate potential algorithms for solving the TSP and compare their performance. [1] Flood, M. M., The traveling-salesman problem. Operations research, 4(1), 61-75, (1956). [2] Martoňák, Roman, Giuseppe E. Santoro, and Erio Tosatti., Quantum annealing of the traveling-salesman problem. Physical Review E 70.5: 057701, (2004). [3] Jain, S., Solving the traveling salesman problem on the d-wave quantum computer. Frontiers in Physics, 646, (2021).