Quantum Optimization for the Graph Coloring Problem with Space-Efficient Embedding

TL;DR

This paper introduces a space-efficient quantum optimization algorithm for graph coloring that significantly reduces qubit requirements, with extensive simulations demonstrating its effectiveness and a comparative study on quantum annealers.

Contribution

A novel quantum algorithm that reduces qubit usage for graph coloring, balancing circuit depth and efficiency, and includes a comparative analysis with quantum annealing.

Findings

Exponential qubit reduction in the number of colors.

Performance demonstrated through extensive numerical simulations.

Quantum annealer study highlights limiting factors.

Abstract

Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient quantum optimization algorithm for the graph coloring problem. Our circuits are deeper than the ones of the standard approach. However, the number of required qubits is exponentially reduced in the number of colors. We present extensive numerical simulations demonstrating the performance of our approach. Furthermore, to explore currently available alternatives, we perform a study of random graph coloring on a quantum annealer to test the limiting factors of that approach, too.