Quantum pricing-based column-generation framework for hard combinatorial problems

TL;DR

This paper introduces a hybrid classical-quantum column-generation algorithm utilizing quantum samplers on neutral atom platforms to efficiently solve complex combinatorial problems like Minimum Vertex Coloring, outperforming some existing methods.

Contribution

It presents a novel hybrid quantum-classical framework inspired by classical column generation, integrating quantum sampling to improve solution efficiency for hard combinatorial problems.

Findings

Achieves good solutions in few iterations

Outperforms some classical and quantum approaches

Demonstrates effectiveness on Minimum Vertex Coloring

Abstract

In this work, we present a complete hybrid classical-quantum algorithm involving a quantum sampler based on neutral atom platforms. This approach is inspired by classical column generation frameworks developed in the field of Operations Research and shows how quantum procedures can assist classical solvers in addressing hard combinatorial problems. We benchmark our method on the Minimum Vertex Coloring problem and show that the proposed hybrid quantum-classical column generation algorithm can yield good solutions in relatively few iterations. We compare our results with state-of-the-art classical and quantum approaches.