AUTHOR=Galda Alexey , Gupta Eesh , Falla Jose , Liu Xiaoyuan , Lykov Danylo , Alexeev Yuri , Safro Ilya TITLE=Similarity-based parameter transferability in the quantum approximate optimization algorithm JOURNAL=Frontiers in Quantum Science and Technology VOLUME=2 YEAR=2023 URL=https://www.frontiersin.org/journals/quantum-science-and-technology/articles/10.3389/frqst.2023.1200975 DOI=10.3389/frqst.2023.1200975 ISSN=2813-2181 ABSTRACT=

The quantum approximate optimization algorithm (QAOA) is one of the most promising candidates for achieving quantum advantage through quantum-enhanced combinatorial optimization. A near-optimal solution to the combinatorial optimization problem is achieved by preparing a quantum state through the optimization of quantum circuit parameters. Optimal QAOA parameter concentration effects for special MaxCut problem instances have been observed, but a rigorous study of the subject is still lacking. In this work we show clustering of optimal QAOA parameters around specific values; consequently, successful transferability of parameters between different QAOA instances can be explained and predicted based on local properties of the graphs, including the type of subgraphs (lightcones) from which graphs are composed as well as the overall degree of nodes in the graph (parity). We apply this approach to several instances of random graphs with a varying number of nodes as well as parity and show that one can use optimal donor graph QAOA parameters as near-optimal parameters for larger acceptor graphs with comparable approximation ratios. This work presents a pathway to identifying classes of combinatorial optimization instances for which variational quantum algorithms such as QAOA can be substantially accelerated.