QAOA of the Highest Order

TL;DR

This paper explores higher order formulations of the QAOA for graph coloring, demonstrating their advantages over quadratic encodings and analyzing their scaling behavior for near-term quantum applications.

Contribution

It introduces higher order problem encodings for QAOA and compares their effectiveness to traditional quadratic formulations, providing insights into their scalability.

Findings

Higher order encodings can outperform quadratic ones in certain graph coloring problems.

Evidence suggests higher order formulations are preferable for specific problem instances.

Scaling analysis indicates potential advantages of higher order QAOA in near-term quantum devices.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) has been one of the leading candidates for near-term quantum advantage in gate-model quantum computers. From its inception, this algorithm has sparked the desire for comparison between gate-model and annealing platforms. When preparing problem statements for these algorithms, the predominant inclination has been to formulate a quadratic Hamiltonian. This paper gives an example of a graph coloring problem that, depending on its variable encoding scheme, optionally admits higher order terms. This paper presents evidence that the higher order formulation is preferable to two other encoding schemes. The evidence then motivates an analysis of the scaling behavior of QAOA in this higher order formulation for an ensemble of graph coloring problems.