Evolving Hard Maximum Cut Instances for Quantum Approximate Optimization Algorithms
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.
Authors 5
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Affiliation as printed
applied Quantum algorithms & LIACS , Leiden University Leiden , The Netherlands
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Affiliation as printed
Optimisation and Logistics , School of Computer and Mathematical Sciences , The University of Adelaide Adelaide , Australia
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Affiliation as printed
Optimisation and Logistics , School of Computer and Mathematical Sciences , The University of Adelaide Adelaide , Australia
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Thomas Bäck Aachen
Leiden University · University of Applied Sciences Leiden
Affiliation as printed
LIACS , Leiden University Leiden , The Netherlands
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Affiliation as printed
applied Quantum algorithms & LIACS , Leiden University Leiden , The Netherlands
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