Quantum Computing for a Profusion of Postman Problem Variants

TL;DR

This paper explores the application of quantum annealing to solve the Chinese Postman Problem and its variants, focusing on problem conversion to QUBO form, algorithm improvements, and empirical evaluation on D-Wave hardware.

Contribution

It introduces a method to convert various Postman problem variants into QUBO form and improves an existing algorithm to reduce complexity, with empirical results on quantum hardware.

Findings

Quantum annealing can solve Postman variants with competitive performance.

Optimized problem encoding reduces the number of variables and constraints.

Hybrid algorithms show promising results compared to classical approaches.

Abstract

In this paper we study the viability of solving the Chinese Postman Problem, a graph routing optimization problem, and many of its variants on a quantum annealing device. Routing problem variants considered include graph type, directionally varying weights, number of parties involved in routing, among others. We put emphasis on the explanation of how to convert such problems into quadratic unconstrained binary optimization (QUBO) problems, one of two equivalent natural paradigms for quantum annealing devices. We also expand upon a previously discovered algorithm for solving the Chinese Postman Problem on a closed undirected graph to decrease the number of constraints and variables used in the problem. Optimal annealing parameter settings and constraint weight values are discussed based on results from implementation on the D-Wave 2000Q and Advantage. Results from classical, purely quantum, and hybrid algorithms are compared.