Multi-Objective Optimization and Network Routing with Near-Term Quantum Computers

TL;DR

This paper proposes a quantum computing scheme using QAOA for multi-objective network routing optimization, analyzing its scalability, challenges, and demonstrating small-scale experiments on a quantum computer.

Contribution

It introduces a novel approach applying near-term quantum algorithms to multi-objective network routing problems, with theoretical, numerical, and experimental validation.

Findings

QAOA can generate Pareto-optimal solutions for network routing

Resource requirements scale with problem size and quantum hardware capabilities

Small-scale experiments demonstrate feasibility on current quantum computers

Abstract

Multi-objective optimization is a ubiquitous problem that arises naturally in many scientific and industrial areas. Network routing optimization with multi-objective performance demands falls into this problem class, and finding good quality solutions at large scales is generally challenging. In this work, we develop a scheme with which near-term quantum computers can be applied to solve multi-objective combinatorial optimization problems. We study the application of this scheme to the network routing problem in detail, by first mapping it to the multi-objective shortest path problem. Focusing on an implementation based on the quantum approximate optimization algorithm (QAOA) -- the go-to approach for tackling optimization problems on near-term quantum computers -- we examine the Pareto plot that results from the scheme, and qualitatively analyze its ability to produce Pareto-optimal solutions. We further provide theoretical and numerical scaling analyses of the resource requirements and performance of QAOA, and identify key challenges associated with this approach. Finally, through Amazon Braket we execute small-scale implementations of our scheme on the IonQ Harmony 11-qubit quantum computer.