Variational and Annealing-Based Approaches to Quantum Combinatorial Optimization

TL;DR

This paper reviews quantum algorithms for combinatorial optimization, highlighting current capabilities, benchmarking results, and potential industrial applications, with a focus on quantum annealing and NISQ-era algorithms.

Contribution

It provides a comprehensive survey of quantum optimization algorithms, benchmarks their performance, and maps them to industrial domains, emphasizing current maturity and future potential.

Findings

Quantum annealing shows highest operational maturity.

QAOA has promising potential on NISQ hardware.

QRL and QGM are long-term research directions.

Abstract

In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the Quantum Approximate Optimization Algorithm (QAOA), Quantum Reinforcement Learning (QRL), and Quantum Generative Modeling (QGM). We then examine the problem classes where quantum technologies currently show evidence of quantum advantage, drawing on established benchmarking initiatives such as QOBLIB, QUARK, QASMBench, and QED-C. These problem classes are subsequently mapped to representative industrial domains, including logistics, finance, and telecommunications. Our analysis indicates that quantum annealing currently exhibits the highest level of operational maturity, while QAOA shows promising potential on NISQ-era hardware. In contrast, QRL and QGM emerge as longer-term research directions with significant potential for future industrial impact.