Evolving Hard Maximum Cut Instances for Quantum Approximate Optimization Algorithms

TL;DR

This paper introduces an evolutionary approach to generate challenging and tractable maximum cut instances for RQAOA, enhancing benchmarking and understanding of quantum algorithms in combinatorial optimization.

Contribution

It presents a novel evolutionary algorithm that creates diverse maximum cut instances in the latent space of a Graph Autoencoder, specifically targeting RQAOA performance.

Findings

Generated diverse graph instances for benchmarking RQAOA.

Identified limitations and strengths of RQAOA compared to classical algorithms.

Expanded understanding of RQAOA's operational boundaries.

Abstract

Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address challenging combinatorial optimization tasks like the maximum cut problem. In this study, we utilize an evolutionary algorithm equipped with a unique fitness function. This approach targets hard maximum cut instances within the latent space of a Graph Autoencoder, identifying those that pose significant challenges or are particularly tractable for RQAOA, in contrast to the classic Goemans and Williamson algorithm. Our findings not only delineate the distinct capabilities and limitations of each algorithm but also expand our understanding of RQAOA's operational limits. Furthermore, the diverse set of graphs we have generated serves as a crucial benchmarking asset, emphasizing the need for more advanced algorithms to tackle combinatorial optimization challenges. Additionally, our results pave the way for new avenues in graph generation research, offering exciting opportunities for future explorations.