Using an \(A^*\)-based framework for decomposing combinatorial optimization problems to employ NISQ computers

Abstract

Combinatorial optimization problems such as the traveling salesperson problem are ubiquitous in practical applications and notoriously difficult to solve optimally. Hence, many current endeavors focus on producing approximate solutions. The use of quantum computers could accelerate the generation of those approximate solutions or yield more exact approximations in comparable time. However, quantum computers are presently very limited in size and fidelity. In this work, we aim to address the issue of limited problem size by developing a scheme that decomposes a combinatorial optimization problem instance into arbitrarily small subinstances that can be solved on a quantum machine. This process utilizes A* as a foundation. Additionally, we present heuristics that reduce the runtime of the algorithm effectively, albeit at the cost of optimality. In experiments, we find that the heavy dependence of our approach on the choice of the heuristics used allows for a modifiable framework that can be adapted case by case instead of a concrete procedure.