Physics

Graph

Limiting

Qubit

Algorithm

Engineering

Optimization problem

Artificial intelligence

Computer science

Quantum computer

Quantum mechanics

Graph coloring

Theoretical computer science

Embedding

Mechanical engineering

Quantum

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.

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