Evolving Hard Maximum Cut Instances for Quantum Approximate Optimization Algorithms
This work addresses combinatorial optimization challenges for quantum computing researchers by providing benchmarking assets and insights into RQAOA's limits, though it is incremental in nature.
The study tackled the problem of identifying hard maximum cut instances for the Recursive Quantum Approximate Optimization Algorithm (RQAOA) by using an evolutionary algorithm with a fitness function to generate challenging graphs, revealing distinct capabilities and limitations compared to the classic Goemans and Williamson algorithm.
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.